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THE  UNIVERSITY  LIBRARY  ('^  iL    i^    '    H 

THE  PENNSYLVANIA  STATE  UNIVERSITY  "s^     ^i      I    /      ,  j 

STATE  COLLEGE,  PENNSYLVANIA 


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THE  EASTERN  OBLIOUE  ARC  OF  THE  UiNlTED  STATES 


OSCULATING  SPHEROID 


TREAvSURY    DEPARTMENT 
U.  S.  COAST  AND   GEODETIC   SUR\^EY 

Sl'PRRINTKNDKN'T 


GEODESY 


THE  EASTERN  OBLIOUE  ARC  OF  THE  UNITED  STATES 


OSCULATING  SPHEROID 


By  CH^S.  J^.  SCHOXX,  ^■'i.ssistant.  Coast  and  Gfeodetio  Survey 


Special  Publication  No.  7 


WASHINGTON 

GOVERNMENT    PRINTING    OFFICE 
1902 


Treasury  Department, 

Document  No.  2232. 
Coast  and  Geodetic  Survey. 


Treasury  Department, 

Office  of  the  Secretary, 

Washington,  J tdy  i6,  rgoi. 
Sir:   It  affords  nie  pleasure  to  approve  the  publication   of   the   discussion   of  the 
Eastern  Oblique  Arc  of  the  United  States,  herewith  presented  to  the  public. 

It  appears  that  the  value  of  this  arc  to  geodesy  is  very  great,  but  that  the  results 
are  only  incidental  to  the  immediate  purposes  for  which  the  triangulation  was  made. 
The  results,  however,  could  not  have  been  obtained  if  the  general  plan  of  the  Coast 
Survey  had  been  less  systematic  or  comprehensive.  Thus,  in  applied  science,  as  well  as 
in  many  other  things,  the  far-sighted  wisdom  of  our  earlier  statesmen,  who  gave  direc- 
tion to  our  beloved  country's  policies,  has  borne  fruit. 
Respectfully, 

L.    J.    G.\GE,  Secretary. 
Mr.    O.     H.    TiTTMANN, 

Superintendent  Coast  and  Geodetic  Siirvcy ,   Wasliington ,  D.  C. 


LETTER  OF  SUBMITTAL. 


Treasury  Department, 
Office  of  the  Coast  and  Geodetic  Survey, 

Washinf^ton ,  D.  CJidy  i6,  /901. 

Sir:  I  have  the  honor  to  submit  to  you  for  pubhcation  the  manuscript  of  Special 
Pubhcation  No.  7,  giving  the  results  of  the  completed  measurements  of  the  Eastern 
Oblique  Arc  of  the  United  States. 

This  is  the  second  of  the  publications  intended  to  give  the  results  of  the  principal 
arc  measurements  made  by  this  vService,  and  like  the  first,  which  relates  to  the  Trans- 
continental Arc  of  the  Thirtj^-ninth  Parallel,  it  was  prepared  by  Assistant  Charles  A. 
Schott,  whose  knowledge,  mature  experience,  and  ability  fitted  him  especially  for  the  task. 

The  Eastern  Oblique  Arc,  though  treated  separately,  intersects  the  Transcontinental 
Arc,  and  the  two  triangulations  have  several  lines  in  connnon.  The  former  extends 
from  the  Bay  of  Fundy  to  the  Gulf  of  Mexico,  and  parallels  the  Appalachian  mountain 
system,  while  the  latter  crosses  the  axes  of  the  great  mountain  systems  of  this  country, 
and  extends  from  the  Atlantic  to  the  Pacific  Ocean. 

Invaluable  as  the  Transcontinental  Arc  is  as  a  contribution  to  geodesy  and  the 
geography  of  our  country,  it  does  not  in  itself  contain  the  data  for  determining  the  figure 
of  the  earth. 

The  Oblique  Arc,  however,  contains  within  itself  all  that  is  neces.sary  for  determining 
the  dimensions  of  a  spheroid  which  corresponds  most  nearly  with  the  existing  geoid 
within  the  area  covered  by  triangulation.  It  is  unique  in  that  it  is  the  first  one  which 
utilizes  on  a  grand  .scale  a  measurement  oblique  to  the  meridian.  The  peculiar  power 
of  an  oblique  arc  for  determining  the  compre.ssion  of  the  earth  was  pointed  out  by  Tobias 
Mayer  (i 723-1 762),  but  the  first  practical  application  of  such  an  arc  to  geodes}' was 
made  by  Bessel.  This  was  before  the  introduction  of  telegraphic  longitudes  had  made 
it  possible  to  utilize  .such  an  arc  to  its  fullest  extent. 

•  The  resvilts  of  previous  di.scussions  of  parts  of  this  arc  led  to  the  abandonment  by 
this  Survey,  in  1880,  of  Bessel's  spheroid  of  reference  and  the  adoption  of  Clarke's  (of 
1866),  and  the  final  di.scussion  of  the  complete  arc  here  presented  .su.stains  the  grounds 
on  which  the  change  from  one  spheroid  to  the  other  was  made. 

Taken  in  connection  with  the  Tran.scontinental  Arc  of  the  Thirty-ninth  Parallel, 
this  discussion  has  enabled  the  Survey  to  decide  upon  the  retention  of  the  Clarke's 
spheroid  and  to  adopt  geographic  coordinates  for  the  whole  extent  of  this  country 
based  on  a  uniform  system.  Fiirther  information  as  to  these  standard  coordinates  for 
geographic  purposes,  which  differ  slightly  from  tho.se  here  published  in  connection 
with  the  Eastern  Oblique  Arc  treated  independently  of  other  triangulations,  will  be 
published  in  due  time. 

Very  respectfully, 

O.  H.  TiTTMANN,  Supcrintoidcnt. 

The  Secretary  of  the  Treasury. 

7 


CONTENTS. 


Page. 

Introduction  19 

PART  I. 
THE  BASE  LINEvS  AND  BASE  NETS. 

A.  General  rem.\rks 25 

B.  The  b.\se   lines   of  the   e.a.stern   oblique  arc,  their  measurement,   resultino 

LENGTH,    probable    ERROR,    AND    ADJU.STMENT    OF    BASE    NETS 27 

1.  Epping  base  line  and  base  net. 

l,ocation,  measurement,  and  length 27 

Adju.stment  of  the  base  net 2<S 

Resulting  angles  and  sides 35 

Descriptions  of  stations 39 

2.  The  Massachusetts  base  line. 

Location,  measurement,  and  length 41 

Connection  with  the  main  triangulation 42 

Descriptions  of  stations 42 

3.  The  Fire  Island  ba.se  line  and  base  net. 

Location,  measurement,  and  length 44 

Adjustment  of  the  1)ase  net   47 

Resulting  angles  and  sides 53 

Descriptions  of  stations 54 

4.  The  Kent  Island  base  line,  base  net,  and  extension. 

Location,  measurement,  and  length 56 

Adjustment  of  the  base  net 58 

Extension  of  the  base  net 63 

Resulting  angles  and  sides 68 

Determination  of  probal:)le  error  in  the  sides  Osbornes  Ruin — Turkey  Point,  and 

Tobacco  Row—  Spear 72 

5.  The  Atlanta  base  line  and  base  net. 

Location,  measurement,  and  length 72 

Adjustment  of  the  base  net 75 

Resulting  angles  and  sides 85 

Descriptions  of  stations 87 

6.  The  Dauphin  Island  ba.se  line  and  base  !iet. 

Location,  measurement,  and  length 90 

Adjustment  of  the  base  net 93 

Resulting  angles  and  sides 97 

De.scriptions  of  stations 97 

C.  Synopsis  of  the  measurements  and   results  of  the  base  lines  of  the  eastern 

OBLIQUE    ARC 100 

9 


I 


lO  CONTENTS. 

PART  II. 

THE  MAIN  TRIANGULATION. 

Page. 

A.  Generai,   treatment  of   The    reduction   of   the   main    triangulation   between 

Calais,  Maine,  and  New  Orleans,  Louisiana 103 

B.  The   TRIANGULATION. 

1.  Northeastern  terminus  to  Epping  base  net 105 

Abstracts  of  horizontal  directions 106 

Figure  adjustment 108 

Resulting  angles  and  sides no 

2.  Epping  base  net  to  Massachusetts  base  and  to  Fire  Island  base  net in 

Abstracts  of  horizontal  directions 114 

Figure  adjustment 122 

Resulting  angles  and  sides 130 

3.  Fire  Island  base  net  to  Kent  Island  base  net  extended 135 

Abstracts  of  horizontal  directions 137 

Figure  adjustment 142 

Resulting  angles  and  sides 145 

4.  First,  or  Virginia  section,  south  of  the  transcontinental  triangulation 148 

Abstracts  of  horizontal  directions 149 

Figure  adjustment 151 

Resulting  angles  and  sides 154 

5.  vSecond,  or  North  Carolina  section,  south  of  the  transcontinental  triangulation 156 

Abstracts  of  horizontal  directions 158 

Figure  adjustment 162 

Resulting  angles  and  sides 163 

6.  Third,  or  South  Carolina  section,  .south  of  the  transcontinental  triangulation 164 

Abstracts  of  horizontal  directions 165 

Figure  adjustment 169 

Resulting  angles  and  sides 173 

Adjustment  of  the  position  of  Mount  Mitchell,  in  North  Carolina 176 

7.  First  .section  west  of  the  Atlanta  ba.se  net 178 

Abstracts  of  horizontal  directions 179 

Figure  adju.stment 182 

Resulting  angles  and  sides 185 

8.  Second  section  west  of  the  Atlanta  base  net 187 

Abstracts  of  horizontal  directions 188 

Figure  adjustment 191 

Resulting  angles  and  sides 192 

9.  Third  .section  west  of  the  Atlanta  base  net 194 

Abstracts  of  horizontal  directions 195 

Figure  adjustment 1 96 

Resulting  angles  and  sides 19S 

10.  Fourth  section  west  of  the  Atlanta  base  net 199 

Abstracts  of  horizontal  directions 200 

Figure  adju.stment 204 

Resulting  angles  and  sides  206 

11.  Fifth  section  west  of  the  Atlanta  base  net 209 

Abstracts  of  horizontal  directions 210 

Figure  adjustment 213 

Resulting  angles  and  sides 216 

Remarks  on  the  accord  of  the  Atlanta  and  Dauphin  Lsland  ba.ses 218 


CONTENTvS.  II 

B.  The  Triangulation — continued.  Page. 

12.  First  section  west  of  the  Daupliin  Island  ba.se  net   219 

Abstracts  of  horizontal  directions 219 

Figure  adjustment •. 222 

Resulting  angles  and  .sides 224 

13.  Second  section  west  of  the  Dauphin  Island  base  net 226 

Figure  adjustment 228 

Resulting  angles  and  sides  232 

14.  Some  statistics  of  the  triangulation 234 

C.  Resulting   Geogr.\phic   Positions  of  the   Principal  Stations   of  the   Triangu- 

lation, Calais,  Maine,  to  New  Orleans,  Louisian.\ 237 

D.  Additional  Geogr.\phic  Positions  which  were  Derived  Differentially  and  for 

WHICH  Triangles  are  not  Given  in  this  P.\per 247 

E.  Additional  Geodetic  Azimuths  Computed  Directly  from  the  Given   Positions 

of  the  St.ations 248 

PART  III. 

THE  ASTRONOMIC  MEASURES. 

A.  Results  for  latitude 

1 .  General  statement 251 

2.  Details  at  stations: 

Agamenticus,  Maine 276 

Atlanta,   Georgia 306 

Atlanta  Middle  Base,  Georgia 305 

Aurora,  Alabama 304 

Bangor,  Maine 257 

Beacon  Hill,  New  Jersey 2S9 

Bull  Run ,  Virginia 292 

Calais,  Maine 253 

Cambridge,  Massachusetts  (Cloverden  Observatory) 282 

Cape  Henlopen,  Delaware 292 

Cape  May,  New  Jersey 292 

Cape  Small,  Maine 271 

Causten,  District  of  Columbia 292 

Charlottesville,  Virginia 292 

Clark,  Virginia 292 

•                    Coast  and  Geodetic  Survey  Office,  District  of  Columbia 292 

Coon,  Alabama 310 

Cooper,  Maine 255 

Currahee,  Georgia 299 

Dover,  Delaware 292 

East  Pascagoula,  Mi,ssissippi 312 

Elliott  Knob,  Virginia 292 

Farmington,  Maine 25S 

Fort  Morgan,  Alabama 313 

Gunstock,  New  Hamp,shire 274 

Harvard  College  Observatory,  Mas.sachusetts  (Cambridge) 2S1 

Hill,  Maryland 292 

Howard,  Maine 263 

Humpback,  Maine 256 

Isles  of  Shoals,  Maine 27S 


1 2  CONTENTS. 

A. — Results  for  latitude — continued. 

2.  Details  at  stations — continued.  Page. 

Kahatchee,  Alabama 307 

King,  North  Carolina 295 

Lavender,  Georgia 301 

Long  Mountain,  Virginia 292 

Lower  Peach  Tree,  AlaVjama 309 

Manoniet,  Massachusetts 284 

Marriott,   Maryland 292 

Maryland  Heights,  Marjdand 292 

Mobile,  Alabama 310 

Montgomery,  Alabama ■ 307 

Moore,  North  Carolina 292 

Mount  Desert,  Maine 264 

Mount  Harris,  Maine 260 

Mount  Independence,  Maine 272 

Mount  Pleasant,  Maine 270 

Mount  Rose,  New  Jersey 290 

Mount  Tom,  Massachusetts 282 

Naval  Observatory  (new).  District  of  Columbia 292 

Naval  Observatory  ( old ),  District  of  Columbia 292 

New  Orleans,  Louisiana 314 

New  York,  New  York 288 

Paris,  South  Carolina 297 

Pooles  Island,  Maryland 292 

Principio,  Marylanci 292 

Ragged  Mountain,  Maine 266 

Rockville,  Maryland 292 

Sabattus,  Maine 269 

Sandford,  New  York 286 

Sawnee,  Georgia 302 

Seaton,  District  of  Columbia 292 

Soper,  Maryland 292 

Strasburg,  Virginia 292 

Sugar  Loaf,  Maryland 292 

Taylor,  Maryland 292 

Thompson,  Massachusetts 279 

Unkonoonuc,  New  Hampshire 278 

Wachusett,  Massachusetts 280 

Webb,  Maryland 292 

West  Hills,  New  York 287 

Yard,  Pennsylvania 291 

Young,  North  Carolina 294 

3.  Summary  of  results  for  latitude 315 

B.  Results  for  longitude. 

1.  General  statement 317 

2.  Results  for  longitude  at  stations: 

Atlanta,  Georgia 318 

Calais,  Maine 31S 

Cambridge,  Massachusetts 318 

Cape  May,  New  Jersey 318 

Charleston,  South  Carolina 318 

Charlottesville,  Virginia 318 

Dover,  Delaware 31S 


CONTENTS.  13 

Page. 

B.  Results  for  longitudk— continued. 

2.  Results  for  longitude  at  stations — continued. 

New  Orleans,  Louisiana 318 

Washington,  District  of  Columbia 318 

Strasburg.  Virginia 318 

3.  Details  at  stations: 

Bangor,  Maine 318 

Charleston,  South  Carolina 321 

Columbia,  South  Carolina 321 

Lower  Peach  Tree,  Alabama 322 

Macon,  Georgia 322 

Mobile,  Alabama 323 

Montgomery,  Alabama 322 

New  Orleans,  Louisiana 323 

Petersburg,  Virginia 320 

Raleigh,  North  Carolina 320 

Seaton,  District  of  Columbia 319 

Statesville,  North  Carolina 319 

Wilmington,  North  Carolina 321 

4.  Summary  of  results  for  longitude 326 

C.  Resitlts  for  azimuth. 

1.  General  statement 327 

2.  Details  at  stations: 

Agamenticus,  Maine 334 

Atlanta  Middle  Base,  Georgia 359 

Aurora,  Alabama 361 

Beacon  Hill ,  New  Jersey 345 

Beaconpole,  Rhode  Island 341 

Blue  Hill,  Massachusetts 339 

Bull  Run,  Virginia 351 

Cape  Henlopen  Light-House,  Delaware 347 

Cape  Sniall,  Maine 332 

Cat  Island  1855,  Mississippi 366 

Causten,  District  of  Columbia 350 

Clark,  Virginia 351 

Cooper,  Maine 328 

Copecut,  Massachusetts 341 

Currahee,  Georgia 357 

East  Pascagoula,  Mississippi 365 

Elliott  Knob,  Virginia 352 

Ethridge,  Alabama 363 

Fort  Morgan,  Alabama 364 

Gunstock,  New  Hampshire 335 

Harvard  Observatory,  Mas.sachusetts 338 

Hill,  Maryland 348 

Howard,  Maine 328 

Humpback,  Maine 329 

Indian,  Massachusetts 340 

Kahatchee,  Alabama 362 

King,  North  Carolina 355 

Lavender,  Georgia 360 

Long  Mountain,  Virginia ■    351 

Marriott,  Maryland 34S 


14  CONTENTS. 

C.   Resui,TS  for  azimuth — continued.  Page. 
2.   Details  at  stations— continued. 

Mar3'land  Heights,  Maryland 350 

Moore,  North  Carolina 352 

Mount  Desert,  Maine 330 

Mount  Harris,  Maine 330 

Mount  Independence,  Maine 333 

Mount  Pleasant,  Maine 334 

Mount  Rose,  New  Jersey 345 

Mount  Tom,  Massachusetts 343 

Paris,  South  Carolina 356 

Principio,  Marjdand 34y 

Ragged  Mountain,  Maine 33 1 

Sabattus,  Maine 332 

Sandford,  Connecticut 343 

Sawnee,  Georgia 358 

Seaton,  District  of  Columbia 349 

Shootflying,  Massachusetts 339 

Soper,  Maryland 349 

Spencer,  Rhode  Island 342 

Sugarloaf ,  Mar3'land 350 

Thompson,  Massachusetts 336 

Unkonoonuc,  New  Hamp,shire 336 

Wachusetts,  Ma.ssachusetts 337 

Webb,  Maryland 34S 

West  Hills,  New  York 344 

Yard,  Pennsylvania 346 

Young,  North  Carolina 354 


PART   IV. 

DETERMINATION   OF   AN   OSCULATING   SPHEROID   FOR   THE    REGION  COVERED    BY 

THE  TRIANGULATION. 

A.  Comparison  of  the  astronomic  and  geodetic  results 369 

1.  The  astronomic  latitude  stations. 

Reduction  to  sea  level 370 

Reduction  for  variation  of  pole 370 

Comparison  of  astronomic  and  geodetic  latitudes 372 

Review  of  latitudinal  deflections 373 

2.  The  astronomic  longitude  stations. 

Comparison  of  astronomic  and  geodetic  longitudes 374 

Review  of  longitudinal  deflections 374 

3.  The  astronomic  azimuth  stations. 

Comparison  of  astronomic  and  geodetic  azinmths 375 

Review  of  azimuthal  deflections 376 

B.  Determination  of    an    oscul.\ting   spheroid    for    the    region    covered   by  the 

TRI.\NGULATION 377 

The  method  and  formulae  employed 377 

Collection  of  constants  and  tabular  quantities  required  in  the  computation  for  estab- 
lishing the  conditional  equations 380 


CONTENTS.  15 

Page. 

B.  Determination   of    an  oscuIvATing   spheroid    for   the    region   covered   bv  the 
TRiANGUtATiON— continued. 

Selection  of  stations  for  which  data  were  admitted  into  the  equatif)ns  of  condition 381 

Conditional  equations  derived  from  latitude  comparisons 385 

Conditional  equations  derived  from  longitude  comparisons 386 

Conditional  equations  derived  from  azimuth  comparisons '. 386 

Formation  of  normal  equations 387 

The  relative  weights  of  the  observation  equations 387 

Resulting  normal  equations  3S8 

The  precision  of  the  adjusted  or  resulting  values  of  the  length  of  the  equatorial  radius 

and  of  the  compression  as  found  from  the  measure  of  the  arc 390 

Resulting  spheroid 391 

Comparison  with  other  spheroids 394 


LLUSTRATIONS. 


Page. 

1 .  United  States  Coast  and  Geodetic  Survey  Office Frontispiece. 

2.  Epping  base.     View  of  line  as  graded  for  measurement 27 

3.  Epping  base.     Placing  base  apparatus  over  mark 27 

4.  Epping  base  net,  Maine 29 

5.  Massachusetts  base,  and  connection  with  tlie  jjrimar}'  triangulation  of  Massachusetts 42 

6.  Diagram 45 

7.  Fire  Island  base  net.  New  York 47 

8.  Diagram 57 

9.  Kent  Island  base  net,  Maryland 58 

10.  Kent  Island  base  and  extension  of  the  triangulation  to  the  westward  and  southward 64 

1 1 .  Ferdinand  Rudolph  Hassler 44 

1 2.  Atlanta  base  net,  Georgia 76 

13.  Alexander  Dallas  Bache 90 

14.  Dauphin  Island  base  net,  Alabama 93 

15.  Diagram 94 

16.  Triangulation,  Epping  base  net  to  northea.stern  terminus 105 

17.  Mount  Desert,  Maine 114 

iS.   Mount  Washington   116 

19.  75-cm.  or  30-incli  theodolite.     Troughton  and  Simms 135 

20.  30-cm.  or  12-inch  theodolite.     Designed  and  constructed  in  the  Instrument  Division,  Coast 

and  Geodetic  Survey  Office 135 

21.  Triangulation,  Epping  base  net  to  Fire  Island  ba.se  net 112 

22.  T'riangulation,  Fire  Island  base  net  to  Kent  Island  base  net,  extended 135 

23.  Triangulation,  first  section  south  of  the  transcontinental  arc 14S 

24.  Triangulation,  second  or  North  Carolina  section 156 

25.  Triangulation,  third  section.  North  Carolina  to  Atlanta  base  net 164 

26.  INIount  Mitchell,  North  Carolina 176 

27.  Triangulation,  adjustment  of  Mount  Mitchell 1 76 

28.  Triangulation,  finst  section  west  of  Atlanta  base  net 17S 

29.  Triangulation,  second  section  west  of  Atlanta  base  net 1S7 

30.  Triangulation,  third  .section  west  of  the  Atlanta  base  net 194 

31.  Triangulation,  fourth  section  west  of  the  Atlanta  ba.se  net 199 

32.  Triangulation,  fifth  section  and  junction  with  the  Dauphin  Island  base 209 

33.  Gulf  coast  triangulation  west  of  Dauphin  Island  ba.se  net 219 

34.  Gulf  coast  triangulation  to  New  Orleans,  Louisiana 226 

35.  Extended  Lambert  equivalent  projection,  showing  the  location  of  principal  arc  measures  and 

areas  of  osculating  spheroids 369 

36.  Naval  Observatory,  Washington,  D.  C 377 

37.  Plan  of  Naval  Observatory  grounds 377 

38.  Subsidiary  telegraphic  longitude  stations  between  Washington  and  New  Orleans 320 

MAPS. 

A.  Area  covered  b}-  the  eastern  oblique  arc  of  the  United  States — triangulation  from  Maine  to 

Louisiana     .    In  pocket. 

B.  Distribution  of  astronomic  stations  along  the  eastern  oblique  arc  of  the  United  States  from 

iMaine  to  Louisiana In  pocket. 

4192 — No.  7 — 02 2  17 


THE  EASTERN  OBEIQUE  ARC  OF  THE  UNITED  STATES,  FROM  MAINE  TO 

LOUISIANA,  kSv.-I'^^Q'^- 


INTRODUCTION. 


The  general  course  of  this  incUned  arc  is  indicated  in  the  title,  and  is  shown  on  a 
projection  with  elliptical  outline  *  facing  Part  IV  of  this  publication.  The  triangulation 
upon  which  it  is  based  begins  at  Calais,  Maine,  on  the  St.  Croix  River,  opposite  the 
Canadian  boundary,  in  latitude  45°  11'  09"'4.  and  in  longitude  67°  16'  ^-"-g  west  of 
Greenwich,  and,  following  the  trend  of  the  Appalachian  chain  of  mountains,  reaches 
the  Gulf  coast  at  Dauphin  Island,  near  Mobile  Bay,  and  terminates  at  New  Orleans, 
Louisiana,  in  latitude  29°  57'  24" "4,  and  in  longitude  90°  04'  24" -4  west  of  Greenwich. 

The  geodetic  line  covers  23°  30'  57",  and  its  total  length  is  2  612-3  kilometers,  or 
I  623"2  statute  miles,  with  an  azimuth  of  57°  3o'7  at  Calais  and  of  223°  22'-5  at  New 
Orleans,  as  counted  from  .south  around  by  west.  Its  extremes  differ  15°  13' 45" 'o  in 
latitude  and  22°  47'  26" '5  in  longitude,  and  in  its  course  it  traverses  sixteen  States,  f 

Near  the  middle  of  the  arc  the  triangulation  crosses  the  thirty-ninth  parallel,  and 
for  .some  distance  in  Maryland  and  Virginia  the  same  triangulation  is  used  in  discu.ssing 
the  oblique  arc  as  was  employed  in  the  discussion  of  the  arc  of  the  thirty-ninth 
parallel,  an  important  feature,  as  will  appear  in  the  following  pages. 

Looking  at  the  gradual  development  of  this  arc,  extending  over  two-thirds  of  a 
century,  it  can  be  .seen  that  in  its  historical  aspect  it  is  readily  divisible  into  several 
well-defined  groups,  and  as  a  whole  it  will  appear  that  its  existence  must  be  ascribed  to 
necessity  rather  than  to  any  preconceived  idea  of  measuring  such  an  oblique  arc. 

Previous  to  the  invention  of  the  telegraphic  method  of  determining  differences  of 
longitude,  first  employed  in  October,  1846,  by  the  U.  S.  Coast  Survey,  in  determining 
the  difference  of  longitude  between  Washington  and  Philadelphia,  and  up  to  a  somewhat 
later  epoch,  when  the  great  accuracy  of  the  method  had  been  fully  demonstrated,  oblique 
arcs  as  well  as  arcs  of  the  parallel  were  held  in  small  esteem  b}'  geodesists,  for  the  reason 
that  the  earlier  methods  did  not  determine  differences  of  longitude  with  a  degree  of 
accuracy  comparable  with  that  obtained  in  observations  for  latitude.  Con.sequently 
their  attention  was  almost  exclusivel>'  confined  in  practice  to  the  measure  of  meridional 
arcs  from  which  to  deduce  the  earth's  magnitude.  Compared  with  an  arc  of  the 
parallel,  an  arc  inclined  to  the  meridian  is  less  fa\-orably  conditioned  for  discussing  the 
figure  of  the  earth  on  account  of  the  greater  effect  of  any  uncertainty'  in  the  measure  of 

*A  Lambert  equivalent  zenithal  projection  extended  over  a  planisphere,  fSee  Map  .\  (in  pocket). 

19 


20  THE    EASTERN    OBLIQUE    ARC. 

azimuths,  and  greater  accuracy  is  demanded  in  the  latter  case  than  is  required  when 
the  arcs  follow  a  meridian  or  parallel. 

Oblique  arcs  should  no  longer  be  regarded  with  any  special  disfavor,  and  while 
they  entail  very  much  more  labor,  comparatively,  when  they  are  utilized  in  determin- 
ing the  figure  of  the  earth,  they  are  well  adapted,  when  of  sufficient  extent,  for  the 
determination  of  an  osculating  spheroid  for  the  region  covered  b>'  them.  The  existence 
of  the  arc  discussed  in  this  publication  is  the  result  of  the  necessity  for  a  main  triangula- 
tion  binding  together  the  detached  surveys  of  the  harbors  on  the  Atlantic  coast  and 
forming  a  base  upon  which  all  subordinate  triangulation  along  the  coast  could  be  brought 
into  accord. 

The  immediate  object  of  the  main  triangulation  was  thus  to  secure  uniformity  and 
systematic  treatment  for  both  the  astronomic  and  geodetic  measures  in  the  preparation 
of  the  geographic  position  of  the  trigonometric  stations.  This  was  a  leading  idea  from 
the  beginning  of  the  Survey  under  its  first  Superintendent,  and  when  fully  developed 
resulted  in  the  work  under  discussion. 

There  could  he  no  doubt  of  the  necessity  of  firmly  binding  together  in  this  way  the 
small  tertiary  triangulation  and  traverse  measures  along  the  coast  which  wind,  unbroken, 
following  the  indentations  of  the  coast,  from  the  Canadian  boundar}'  to  Cape  Florida 
and  thence  into  the  Gulf  of  Mexico,  following  the  coast  to  the  Mexican  boundar}'. 

The  measurement  of  the  oblique  arc  was  thus  identical  with  the  progress  of  the 
ordinary  operations  of  the  Survey  in  this  portion  of  the  country. 

The  first  period,  covering  the  years  1833  to  1844,  witnessed  the  executicjn  of  the 
work  from  central  Long  Island,  New  York,  to  the  head-waters  of  Chesapeake  Bay, 
uniting  on  the  way  the  surveys  at  New  York,  New  York,  and  Philadelphia,  Pennsyl- 
vania, and  this  work  was  nearly  all  completed  under  Superintendent  Hassler. 

During  the  second  period  Superintendent  Bache,  pursuing  the  same  general  plan, 
had  the  work  carried  from  Rhode  Island  to  the  Canadian  boundary,  at  Calais,  Maine,  on 
the  St.  Croix  River,  and  this  work  was  completed  in  1859. 

In  1865  the  branch  primary  triangulation  across  the  State  of  Connecticut,  connect- 
ing the  main  scheme  with  some  older  work  in  this  region,  was  completed.  This  period 
closed  in  1871,  when  the  Potomac  River  was  reached  and  crossed. 

In  the  third  period,  covering  the  years  1873-1877,  the  work  was  extended  to  the 
Atlanta  base,  in  Georgia. 

The  fourth  period  begins  in  1885  and  extends  to  1898,  and  during  this  time  the 
work  was  extended  to  Mobile,  Alabama. 

The  triangulation  between  Mobile  and  New  Orleans,  Louisiana,  was  done  between 
1846  and  1874. 

While  the  field  work,  as  completed,  apparently  covers  a  very  long  period,  the  first 
measures  dating  back  to  the  year  1833  and  the  last  measures  being  made  in  1898,  as  has 
been  stated,  this  interval  contained  many  years  when  no  work  was  done  upon  this  arc. 
The  slow  rate  of  progress  was  thus  onlj'  apparent,  as  it  depended  upon  and  was  subor- 
dinate to  the  ordinary  requirements  of  the  Survey  on  this  part  of  the  coast,  and  of  the 
general  operations  of  which  it  was  only  an  incidental  feature. 

Part  I  deals  mainly  with  the  base  lines  and  Part  II  with  the  intervening  triangu- 
lation. 

The  astronomic  determinations  of  latitude,  longitude,  and  azimuths  are  numerous 


ULl 


INTRODUCTION.  2  1 

and  well  distributed  over  the  whole  arc.  There  are  a\ailable,  for  the  computation  and 
comparison  of  geodetic  and  astronomic  positions,  results  at  71  latitude  stations,  at  17 
longitude,  and  at  55  azinuith  stations.  The  latitudes  depend  almost  exclusively  on 
observations  with  zenith  telescopes,  and  the  longitudes  on  telegraphic  transmission  of 
time.  The  azimuths  depend  upon  a  variety  of  methods,  using  the  pole  star  most 
frequently.  Abstracts  of  the  individual  and  final  results  of  the  astronomic  measures 
are  presented  in  Part  III  of  this  publication.  The  distribution  of  the  astronomic 
stations  over  the  region  covered  by  the  arc  is  shown  on  Map  B  (in  pocket),  and  the 
two  maps  A  and  B  have  the  .same  scale  as  the  similar  maps  accompanying  U.  S.  Coast 
and  Geodetic  Survey  Special  Publication  No.  4,  containing  the  discu.ssion  of  the  trans- 
continental arc  of  the  parallel  in  latitude  39°  N. 

Part  IV  contains  the  comjiarison  of  the  geodetic  and  astronomic  measures  and  the 
determination  of  an  osculating  spheroid  for  the  region  covered  by  the  arc. 

Preliminar}-  publication  of  the  greater  portion  of  this  arc  has  already  been  made  in 
the  following  reports  of  the  vSurvey:  Report  for  1865,  Appendix  No.  21,  pp.  187-203, 
' '  Results  of  the  primar\-  triangulation  of  the  coast  of  New  England  from  the  north- 
ea.stern  boundary  to  the  vicinity  of  New  York;"  Report  for  1866,  Appendix  No.  8, 
pp.  49-54,  "Report  on  the  geodetic  connection  of  the  primary  base  lines  in  New  York 
and  Marjdand,  their  degree  of  accordance  and  accuracy  of  the  primary  triangulation 
intervening,  with  the  resulting  angles  and  distances  as  finally  adjusted,"  and  Report  for 
1878,  Appendix  No.  8,  pp.  92-120,  "On  the  adju.stment  of  the  primary  triangulation 
between  the  Kent  Island  and  the  Atlanta  ba.se  lines. ' '  These  reports  contain  also 
more  or  less  complete  accounts  of  the  six  ba.se  lines  located  in  the  arc. 

Other  references  will  be  given  in  their  proper  place.  The  present  publication  i.s 
complete  in  itself,  and  while  no  important  facts  or  statements  are  om'itted,  much  .simpli- 
fication has  been  effected  by  referring  to  the  publication  above  mentioned,  covering  the 
transcontinental  arc  of  the  parallel,  the  same  general  treatment  and  method  of  reduction 
of  the  triangulation  having  been  emplo>'ed  in  reducing  that  arc  as  is  u.sed  in  the 
following  discussion  of  the  oblique  arc. 


J 


P  A  U  T    I . 


Till-:  BASl'   LlXl'.S  AM)  BASl:  Xl-TS. 


i 


Till-;  I'.ASi-;  \.\\\'s  WD  l;\^l;  \n\ 


A.  (•.1'',.\i:r.\i,  ri-.marks. 

Tlu-  tinil  of  length  i>  tlu-  Mime  ;i>  tlial  u.^cii  Iroin  tlic  l)c;(iniiiii^  oi  tlie  Survey  until 
iH.Scj,  \i/.,  an  iron  l)ar,  i  lut-tcr  luni;,  standardized  at  Paris  in  ijvy  and  (jrou^jht  to  this 
coinilry  by  Mr.  I''.  K.  Ilassler  in  1S05.  Its  use  was  discontimied  after  the  receipt  ut  tlie 
new  i)n)t()type  ])lalinnni  meters  in  November,  issi^.  This  meter,  known  on  the  Survey 
a.s  the  Committee  Meter,  is  an  end  measure  and  is  rejjreseuted  by  an  iron  iKirwith  .s^juare 
end  snrfaies,  now  r.li^lilh  (Ufaced  by  corrosion  and  jierliaps  liy  u.se.  It  will  suffice  to 
refer  the  reader  to  the  fnll  account  .t^iven  of  this  meter  ni  Part  I  of  the  '  Tran.sconti- 
neMilal  'rrianL^nlaiioii  and  the  .\merican  Arc  of  the  Parallel  "  across  the  I'nited  State>  in 
the-  \icinil\  of  lalitnde  31/,  i)iii)lished  by  the  Coast  and  C.eodetic  Survey  in  i<ttji>.  In 
that  pnbliialiou,  after  some  liistorical  notes,  the  results  of  the  lunnerous  comparisons, 
direct  am!  indirect,  1)\  different  ol)ser\-ers,  liy  diderent  methods  and  at  different  times. 
are  coniiiklel\  set  forth,  and  the  hnal  conclusion  is  reached  that  this  bar  at  u"  C.  repre- 
sents so  neaiTv  the  lenL;th  of  the  i)rotot>i)e  meter  that  no  relial)le  value  of  the  difference 
can  be-  slate-d.  TMie  weii^iited  mean  of  all  e-omparisons  ,uave  the  result  i  ^o-2Hzi:o6n, 
and  in  all  eiinipr.lalions  dependin.n  upon  this  .standard  it  has  Injeu  taken  as  etjual  iti 
len.i;tli  to  the  proiotspe-  meter  with  a  probable  error  of  about  three-cjuarters  of  a  micmn. 

There-  are  six  base  lines  irrefjularly  distributed  aloni;  the  arc.  and  they  are  descril>e<l 
in  the  order  of  location,  bci^^inniny:  in  the  extreme  northeast  ami  eudiui;  on  the  CiUlt 
coast.  h'or  eaeli  line-  all  needful  information  is  j.;iven  in  ce)unectiou  therewith,  such  a.s 
position,  i)hysical  features,  elevatie)n  .d)o\e  sea  level.  api>ar.UUs  useel  for  the  measure, 
nan'ie  of  observer,  com])Utation  e)f  len.i;lh  and  hnal  result,  with  its  proKible  erre>r. 

.V  sketch  of  each  base  net  is  jiresented,  and  it  is  followeel  by  the  abstracts  of  hi>ri/on- 
lal  dire-e'tions,  obse-rxcd  and  adjusted,  for  e.ich  station  forming;  i>art  of  the  net.  These 
absiiaets  e-onlain  the-  following;  inform, ition:  Count\-  anil  State,  elate  of  measure,  inslru- 
nie-iU  Used  and  olisei\e-r's  n.inie,  ,ind  also,  in  the  first  e-olinnn,  the  lUunlKT  of  each  ilirec- 
tion.  Tlle-^e  nmnlu-is,  when  in  iKUenthescs.  in  licite  the  correspomliui;  eX)rrections  as 
,i;i\en  b\  llie-  net  ,hljn>lnunt .  In  the  ,L;re-al  majoriiv  oi  ca.ses  liinr/ion  thetHlolites  were 
eiiijilov  ed.  and  foi  ilie-se  iRSSels  method  '  <.A  reiluction  at  the  station  was  usetl.  When 
/■(-/>(-<?//Wi,'  theodolite's  were  iise-d  tile  statiem  adjustment  foUmveel  the  onlinary  nietluKl  ■»' of 
eHMubination  with  ilu-  iiUit>duction  <.A  relative  weights.  HeK>w  the  aKstracts  of  ilirtvtions 
resultiiiL;    fioiii  st.uion  .uljiislment    there  is  i;iven  the  probable  err«>r  of  a  simple  obscn'a- 

*  Sio  W  W .  \\  riijlil's  "  'rri'iUisc  on  tlu'  .\iljii-.lnunt  of  Olwcn-atioils."  New  V,<rl„,  isn4    ;>■ 
t  Uiiil.,  p    1  >)  .nul  foil  .  al>a  )>    Ji:  .itul  toil. 


26  THE    EASTERN    OBLIQUE    ARC. 

o'455  5'J' 
tion  of  a  direction  (mean  of  the  direct  and  reversed  series)  deduced  from  (?,'=  —  ,-.-—  , 

where  ;/  =  number  of  observations,  ^  =  number  of  series,  d  =  number  of  directions,  and 
J=  diiferences  of  observed  and  adjusted  vahies. 

The  figure  adjustment  of  the  triangulation  generally  proceeds  on  the  supposition  of 
equal  weights  to  all  directions  used  in  the  adjustment,  except,  as  in  the  case  of  the  Epping 
base  net  adjustment,  where  special  weights  are  introduced.*  To  carry  weight  equations 
from  the  station  adjustment  into  the  figure  adjustment  is  not  practiced  or  favored  in  the 
Survey  on  account  of  the  increased  complexity  and  the  doubtful  advantage  of  the  pro- 
ceeding. The  errors  brought  to  light  by  geometrical  conditions,  and  which  have  been 
called  triangle-combination  errors,  are  of  a  different  character  from  those  developed 
by  a  comparison  of  the  measures  made  at  a  station,  where  defects  of  centering  at 
observing  and  observed  stations,  effects  of  large  local  deflections  of  the  vertical  at  a  sta- 
tion, persistent  lateral  refraction  along  a  line,  etc.,  do  not  .show;  that  is  to  say,  weights 
pertaining  to  one  operation  are  not  those  proper  for  the  next  operation.  Further  par- 
ticulars of  figure  adjustment  with  statement  of  formulae  may  be  found  in  "The  Trans- 
continental Triangulation,"  Part  I. 

Foi  the  computation  of  the  sides  of  the  triangles  Legendre's  theorem  was  used, 
and  since  none  of  the  lines  of  the  oblique  arc  are  very  long  the  .spherical  excess  was 
computed  by  the  simple  formula 

ab  sin  C 
2/3^  p„  sin  i" 

where  C  =  the  plane  angle  included  by  the  .sides  a  and  b  and  the  subscripts  to  ft  refer 
to  the  radius  of  curvature  in  the  meridian  and  in  the  prime  vertical.  Appendix  No.  9, 
Coast  and  Geodetic  Survey  Report  for  1894,  page  291,  contains  a  table  to  facilitate  the 
computation  of  the  spherical  excess,  the  argument  being  the  latitude  of  the  center  of  the 
triangle.  The  computation  of  the  geodetic  positions  along  the  oblique  arc  is  made 
according  to  the  formulae  and  tables  in  the  same  appendix,  the  differences  in  latitude, 
longitude,  and  azimuth  for  two  points  of  known  distance  and  azimuth  being  given  by 

[  ~Aqj  —  s  cos  a.  B-\-s-  sin'  a.  C-\-{,Sq)y  D—h  r  sin'  a.  E 

I       A\  —  s  .sin  a  sec  q)' .  A 

\-Aa  =  A\  sin  >4  (<p+<^')  .sec  Y^  (^9)+  (^A.)='  F 


where 

(p'-(p-^Aq) 

A'  =  A.+z/A 


■a.wA—8qj  —  s  cos  n.  B-\-s'  sin'^  a.  C—kr  sin''^  a.  E 
also  h  =  s  cos  ix.  B. 


The  factors  A,  B,  C,  D,  E,  and  /^are  tabulated  and  refer  to  Clarke's  spheroid  of  1866. 
Their  logarithmic  values  are  given  for  every  minute  of  angle  between  latitudes  of  18° 
and  72°. 

A  description  of  each  station  u.sed  in  the  base  nets  is  given.  The  description  of  the 
other  stations  of  the  triangulation  can  be  obtained  upon  application  to  the  Coast  and 
Geodetic  Survey,  Washington,  District  of  Columbia. 


*When  special  weights  are  introduced  for  the  several  directions  at  a  station,  they  are  deduced  from  the  rough 
-ession  of  the  square  of  the  probat: 
the  direction  in  the  normal  equation. 


expression  of  the  square  of  the  probable  error  given  bj  ei^=     ^  r'^^. —  where  [xx]  represents  the  diagonal  coefficient  of 


It 


4i 


Pi^    i&     I  ^, 


HASI',    LINKS    AM;    I'-ASH    NI-'.TS.  27 


ii.  'riii'.  I'.ASJv  i.ixivs  oi'  'I'iii'.  I'.As'n.RN  ojiijorj-.  arc  thiuk  mi-:as- 
ruivMiCNT,  i<i:sri;ri.\r,  ij:.\(/i"n.  rkoi'.Ai'.ij-:  i-;Kkfjk, 

AND   ADjrSTMIvN'l'  OI-    liASI'".   NJ/fS. 

I.    rill,   i.im-im;   hasi'.   i.i.M';  ani>  hash  nkt,  maink,  1H57. 

Locdtioii ,  iiintsiirriiiiii/ ,  and  iisitllitii^  Iciii^lh  of    thr  Jippi/K/  i>a^(  linr,  Mairit' .  iS^y. 

Tlu-  silL-  ot  lliis  Itasc  is  on  ]vp])in^  I'laiiis,  near  ClK-rryfield.  Wa^IiiiiKton  Counly, 
Maine.  A  reconnaissancx-  of  the-  locality  was  made  in  is.s.v  'I'xl  tl>^'  iiieasurcinciit  of 
the  base  followed  in  Jtd\-  and  August,  1S57,  under  the  immediate  direction  of  Sujxrriji- 
tendeiil  A.  I).  Hache.  Tlu-  Aiiiiiia!  Ri|)(.rt  for  1.S65,  A])ix:iidix  N(j.  21,  pa^es  i?i9-iyi, 
contains  a  full  acc(Jinil  of  the  measure  and  of  the  result.  It  will  therefore  suffice  to 
present  here  onl\'  the  .salient  points  of  the  o])eration. 

The  measure  was  made  wilii  the  Hache-Wurdeinann  contact-level  coiniHrii.sating 
a])paratus,  and  is  the  sixth  primary  line  where  this  ajjparatus  was  emj)loyed.  the  Dau- 
])hin  Island  base,  Alabama,  beini;  the  first,  an  account  of  which  is  given  further  on  ( ij.  v.  ;. 
The  apparatus  is  fully  descril)ed  with  illustrations  in  Coast  Survey  Rejxjrt  for  i''^54. 
Appendix  No.  35,  and  reprinted  in  Coast  vSurvey  Rejiort  f(jr  1.S73,  ApjKrndix  No.  i.;. 
The  essential  ])art  of  the  ajjparatus  consists  of  two  6-meter  bars,  (jne  of  bra.ss  and  one  of 
iron,  placed  jjarallel  to  each  other,  one  being  abo\e  the  other  and  firmly  coiuiected  at 
one  end.  At  the  (opposite  or  free  end  is  the  lever  of  com{)ensation.  so  pro|Kjrtioned  in  its 
arms  with  respect  to  the  actual  and  differential  expansion  and  contraction  witli  changes 
of  temi)erature  thai  the  end  of  liie  ap])aratus  Iemain^  at  a  constant  distance  from  the 
opposite  end.  The  spirit-level  contact  piece  terminates  in  an  agate,  ground  to  a  knife 
edge,  whereas  the  agate  at  the  ()])posite  presents  a  slightly  convex  surface.  The  appa- 
ratus was  standardi/eil  1)\  niean>  of  a  standard  6-meter  iron  bar.  the  length  of  which 
was  determined  at  dilTeient  times  in  terms  of   the  Conunittee  Meter. 

The  length  of  this  base  is  about  S'yj  kilometers  (  or  5'4_'  statute  miles  ■,  its  middle 
point  is  in  latitude  44°  4o''S  and  in  longitude  67''  53''.  with  a  mean  a/.imuth  of  iij6° 
54'.  Much  labor  had  to  be  spent  prei)aring  the  groinid  for  the  measure  by  leveling  it. 
removing  l)owlders,  and  overcoming  other  obstacles,  the  handling  of  the  apjuratus 
deuianding  a  wide  and  fairly  smooth  roadwax  ,  The  average  height  of  the  tuivs  aUive 
the  mean  tide  level  of  the  Atlantic  was  7(>"4,s  meters.  The  d-meter  kise  l*ars  or  tulx.-s 
were  compared  with  the  standard  o-meter  bar  just  before  and  inuiiediately  after  the  Ui.se 
measure.  Taking  the  lcii'-;th  of  ilie  latter  and  ilscoefiicieiu  of  expansion  as  ileterniineil  in 
i860  and  published  by  Assistant  J.  \\.  Hilgard  in  Coast  Survev  Report  t\>r  iSfu.  ApjK-ndix 
No.    26,  viz,  .S'yijij  941  meters,  and  o'ooo  01  1  54  for  the  centis^raile  scale,  the  following 

residls  for  the  length  of  the  tubes  were  obtaineti:  Three  sets  of  23  comp;iri.s*.)ns.  made 
with  Saxton's  letlecting  ci)mparat(»r  ■■  on  July  toth  and  17th,  gavetulK-  No.  i  shorter  than 
the  stand, 11  d  I  at  iS''3C.)  1  3LxV4ilivisions  of  the  compar.\tor  and  tulv  No.  .'shorter  1  (."kSS" 7 

±-'o  i:  z'2 


*  Tin  iii-ti  vimvnl  i>  kimwn  ii-.  Siixtons  pyrometer,  ami  it  i>  aocrilxnl  in  drtiiil.  with  ilUi.'>(rnlii>iiv  in  the  Report  of 
thf  SuptTiiUcmlciit  of  WtiKlUs  ami  Mias>irc<  lor  is.i^  ami  thr  Kcjx>rt  of  the  >iniic  Imrcau  for  !■♦.•  cvtmainv  on  {vi^r  ir<, 
n  miicral  lU-scription  of  it.     Out-  larii  of  the  screw  equals  ,v.'i7ii  scnle  ilivisioiis  nml  one  <u.-nlr<li\-iMonc\|iMl>  t\;r  niu-rxiti*. 

Tho  hfjul  \*i  vliviiU-tl  into  ux>  tlivisious. 


28  THE    EASTERN    OBLIQUE    ARC. 

divisions;  again,  after  the  base  measure,  on  August  6th  and  yth,  from  4  sets  of  27  com- 
parisons, tube  No.  I  shorter  than  the  standard  (at  2i°'oC.  )  i  411 '8  divisions  and  from 

±  3-3 
4  sets  of  23  comparisons  tube  No.    2  shorter  i   195 '3  divisions.      Having  regard  to  the 

=h2"9 
weights,  the  abo\'e  comparisons  give  the  vahies  for  length  of  tubes, 

for  No.   i„,  5 '999  459  o  meters,* 

±49 
for  No.  2,   5 '999  750  6  meters. 

±49 

Although  the  comparisons  of  the  tubes  with  the  standard  bar  were  made  with  rising  and 
falling  temperatures,  there  remained  an  uncertainty  respecting  the  indication  of  the 
thermometers  in  air  giving  the  temperature  of  the  metallic  bar  even  within  }^° .  Furtiier, 
some  allowance  had  to  be  made  for  any  defect  in  the  mechanical  compensation,  for  pos- 
sible error  in  making  contacts  and  transfers  to  the  ground,  and  for  other  small  uncertain- 
ties in  connection  with  the  base  measure,  and  this  was  arbitrarily  fixed  as  ±  g'j  /<.  The 
probable  error  of  the  length  of  a  tube  during  the  measure  was  taken  as  ^ji^'g)-  +  (g'j)'^ 
=  =t  io'9  yu,  hence  that  for  the  whole  length  =  i  453  X  io'9  yU  =  o"oi58"',  which 
equals  55X650  pai't  of  the  length.  In  this  case,  as  in  that  of  the  other  bases  of  this  arc, 
except  the  Atlanta  base,  the  single  measure  fails  to  provide  proper  means  for  a  more 
reliable  value  of  the  probable  error  of  the  length.  We  have  for  the  length  of  the  Epping 
base: 

I  452  tubes  of  mean  length,  8  711"' -4262 

One  odd  tube.  No.  i,  +5'9994 

Correction  for  inclination  of  tubes,  — 2'So40 

Defect  of  last  tube  at  East  Base,  -fi'425o 

Reduction  to  half-tide  level  of  ocean,      — o'i044 

Resulting  length  of  base,  S  7i5"'-9422  rb  o""oi58 

And  its  logarithm,   3'9403i434  ii=  o'oooooo79 

The  Eppiuij  base  net  and  results  of  its  adjustment. 

As  shown  on  the  following  sketch,  this  net  of  triangles  is  included  within  the 
primary  quadrilateral  Humpback,  Mount  Desert,  Howard,  and  Cooper,  and  involves  6 
geodetic  points.  The  figure  is  a  ver>'  strong  one  and  demands  that  35  geometric  con- 
ditions be  satisfied.  The  reduction  of  this  base  net  is  complicated  on  account  of  the 
employment  of  both  direction  and  repeating  theodolites,  five  of  the  stations  having  been 
occupied  with  the  latter  instruments. 

An  account  of  the  adju.stment  of  this  base  net  iscon,ained  in  Coast  Survey  Report  for 
1864,  Appendix  No.  14,  and  may  be  referred  to  for  particulars;  the  results  are  here 
transcribed,  except  that  the  notation  has  been  changed  for  one  more  convenient.  In 
connection  with   the  station   abstracts  there  is  added  a  column  containing  the  approxi- 

*Comparing  these  values  with  the  corresponding  values  of  1847  (Dauphin  Island  base)  and  of  1872-73  (Atlanta 
base),  it  will  be  seen  that  the  lengths  are  not  invariable,  but  it  should  be  noted  that  one  of  the  agates  of  tube  i  was  acci- 
dentally broken  in  1855,  and  after  the  new  agate  was  substituted  the  tube  was  found  to  be  o'43o  millimeter  shorter  than 
before. 


Coop«^> 


Jhiniphnrk 


IIASI',    I.IN'I-.S    A  NO    I'.ASK    NKTS.  29 

mate  value  of   tlic   ])rol»;il)lc  crnd'  ol    a   resiillin^   'lircctioii,  deiKrii'lintc   on   tiic-  I'ortmila 

o'455  ^/i  .....  ... 

^ -■ ..      -p-^.' „,      in  case  ot  (lirccliou  ohscr\'atioii'i.       In    <.a>>c  ol   r<-ix:titi'jn>i  the  nroli- 

s  (ciiag.  cocli  ij  '  ' 

alilc  error  will  (le])en(l  ui)on  the  cotnparison  oi  a  reTiiltin;^  an^le  with  each  of  its 
20  measures  Teacli  of  3  repetitious  direct  and  3  rejietitions  reversed;,  from  which  an 
averajre  and  a])])roxiniale  '.alue  r,t  the  probal»le  error  of  a  v///;'/^'  measure  of  an  ant<le 
aud  of  a  direclicjii  lias  been  deri\ed,  as  well  as  the  jjnjbahle  error  of  a  rtsullim^  direc- 
tion. We  liave  a])])roxim:itely  ^,^ 
fioni  tlie  20  measures  of  each 
aui^le  the  i)rol)al)le  error  oi  a 
single  observation  of   an  auf^le 

f         "'•'^  IS     ;      ,  ■•■  hence 

the  jjrobable  error  of  a  sinj^le 
observation  (3  D.  and  3  A*.  )  of  a 
direction  r^  --c'^/\J2,  also  ap- 
])roxiniatel3''  for  a  ^e^ulting• 
direction  f^  -^fJyJ20.  The  last 
colunui  of  the  abstracts  con- 
tains the  fnial  adjusted  direc- 
tions, the  lirst  direction  hax'inj;' 
aj^aiu  l)een  made  zero  !)>■  sub- 
tractin<;  the  correction  to  the 
initial  direction  from  v:\c\\  of 
the  corrections  to  the  other 
directions,  as  ,i;i\rn  in  the 
precedinj;  colunui.  i 

In  the  adjustnu'iil  of  the 
ba.se  net  special  wci.^hts  were 
nssij^ned  to  the  directions,  as 
exiilaiucd  ,it  U'ni;tli  in  Coast 
vSurve>  Repot  t  for  lS(>(.  If 
we  lU'duce  the  probable  el  loi  of  a  direction  from  the  closiuv;  errors  in  the  xum  of  the 
auL^Ksol  the  40  Iriaui^les,  we  liud    from  the  sum  oi  iIk-  >t|U. ires  of  iJK-.-e  irror->  the  mean 

closiiis;  ciroidf  a  tri.niL;lc       ./■''"*  ^'  -;  rt  i"'oo,   hence   the   proUible  error   of  a   direc- 

>      46  ' 

tion  =  0(174  \  1  00  y'o   -  zfco"'3o, 

On  the  other  hand,  the  avera.i^e  value  of   the  jiroliable  error  of  obser\Mtioii  oi   the 

11(1  directions    in    the    net    is  about  rt  o""J4,    whence  the   triaui^le  combination  error 

*,  -    v(,o"3o)°— (o*24)-"  —  ±o""i7   tnearlx  b    and   the   square   oi   this  was  adtleil   as  a 

rcz/.s-Ar/// to  each  ol    the   prexiously  deduced  squares  of   the  olwervitiii  errors.      W'c  then 

have    >■-'       ■'      •    ."      ind  the  weii^lu  to  ,ui\  directiini  p  The  values  i>f  />  thus  have 


*Tln-  hnlf  l>nioktt  iiiilioatfs  sum  »f  siiiiiliir  (lUiiMlitic".  ilisri-ijanlinij  their  sirh- 

tl'ho  lucaii  of  till'  .|  vahu-s  of  ,-,  .U-nvi<l  frviii  11  -iiiKU-  mcsisun-  . />  rtiul  A"  1  with  ihc  -s  "  thcvxlolilr  i»  -  t  '  v\4 
nml  •!»•  mean  of  tin-  s  valius  v>f  r-i  lUrivnl  from  a  siii(;U-  iiua»urc  (.;/>.  ami  sA"  ■  with  the  .-v"-  tr{)ratiii|;  (hcuiMilr  i» 
A  i"i(>,  or  one  measure  with  the  first  instniiiieiit  is  alxjiit  et|iial  in  acv-nnu-y  to  three  with  the  latter. 


30 


THE    EASTERN    OBLIQUE    ARC. 


smaller  range  than  the}'  would  have  had  without  the  addition  of  the  constant;  still 
the  maximum  weight  is  to  the  minimum  weight  as  5  "4  to  i.  The  effect  of  the  intro- 
duction of  weights  is  small  in  cases  like  the  present,  a  base  net  of  great  complexity 
and  fair  measures. 

There  was  no  special  necessitj^  for  a  reduction  of  the  horizontal  measures  to  sea 
level  on  account  of  the  elevation  of  the  signals  sighted.  The  following  table  gives  the 
approximate  heights  of  the  ground  at  the  stations: 


Meters. 

Feet 

Epping  East  Base, 

77-6 

255 

Epping  West  Base 

.    72-9 

239 

Burke, 

1295 

425 

Tuiik, 

350-5 

I   150 

Pigeon, 

95  "9 

315 

Humpback, 

451 

I  480 

Mount  Desert, 

464-9 

I  525 

Howard, 

82-0 

269 

Cooper, 

224 

735 

The  largest  reduction  for  latitude  45°  and  «  =  45°  ( nearlj'  that  of  the  line  Epping 
East  Base  to  Motmt  Desert)  would  amount  to  only  o"-o25,  a  correction  so  small  that  it 
may  be  neglected. 

Abstracts  of  resulting  horizontal  directions  observed  and  adjusted  at  stations  forming  the  base  net, 

1S56-1S59. 

Eppin<j  East  Base,  Washington  County,  Maine.     September   17  to  September  29,  1859.     25""  repeat- 
ing theodolite  No.  43.     C.  O.  Bcaatelle,  observer.     Telescope  14  meters  above  ground. 


No.  of 
direc- 
tions. 

objects  obser%-ed 

I 

Mount  Desert 

2 

Burke 

3 

Tunk 

4 

Epping  West  Base 

5 

Humpback 

6 

Howard 

7 

Pigeon 

Re.sulting      direc-       Approxi- 
tions  from  station     mate  prob- 


Corrections        Final 
from  base       seconds 


adjustment. 

able  errors 

nee  aajusi- 
ment. 

gulation. 

0       / 

// 

// 

// 

// 

0     00 

00 -oo 

±0  -27 

GOOD 

GO  '000 

13     34 

42-40 

0-28 

-0  -556 

41  -844 

39     21 

25-46 

0-27 

+  1  -035 

26  -495 

65     II 

55-30 

0-31 

-0  -476 

54  -824 

92     52 

56-31 

0-28 

— 0-I57 

56-153 

235     22 

32-46 

0-28 

-0  -582 

31  -878 

329    07 

59  -So 

0  -29 

—0  -878 

58  -922 

%  R.)  of  a  direction,  e^  = 

±o"-94.     Number  of 

angles  adjusted,  14. 

Epping    West  Base,  Wasliington  County,   Maine.     October  11   to  October  16,   1859.     25'"'  repeating 
theodolite  No.  43.     C.  O.  Boutelle,  observer.     Telescope  14  metters  above  ground. 


8 
9 

ID 
II 
12 


Epping  East  Base 

Pigeon 

Burke 

Tunk 


Humpback 

Probable  error  of  a  single  observation  {3/^.  and  3  7?. )  of  a  direction,  fi 
angles  adjusted,  6. 


0 

00 

00  -00 

±0-19 

0  -000 

00  -ooo 

64 

55 

08-30 

0  -20 

+0  -951 

09-251 

89 

03 

11.75 

0-25 

—0  -422 

II  -328 

38 

04 

57-08 

0-23 

—0122 

56  -958 

17 

36 

38-06 

0-24 

+0-551 

38-611 

d=o''''-96.     Number  of 


I'.ASl-.    I.INl.S    AM)    I'.ASIv    NKTS. 


.V 


yl/islnitl.s  (if  icsit/luix  hill  i::t)ii!iil  din-ilioiis  ohsfivrd  and  udjiidfd  cil  ■ilatiom  Ji>imtni(  tht-  hate  iii't , 

/.V5<5-/.V5(>---continue'I. 

Iiurl<t\   VVashinj^toii   Coiiiil)',   Maine,      Si-pU-iiilxr  yt  lo   Oilrjix-r    \u,    1X59.      25  *  rci>ealin>»  the<*lolitc 
No.  43.     C.  ().  I'.oiitL-llL-.  oljservcT. 


No.  of 
direi- 
tioiis. 


((liJL-ils  oliservi-il. 


HesultinK,|ir.c  Ap,.roxi        S'r'onT'r:^'         '" 

lioiii  from  -.lalK,!!      male  \,r>,\,      ,,^."",1?,,^ 

Illrllt 


pp. 
.'KljustmeiU  .iMc  crrori 


r3  I  1  Iuin]il):ick 

14  I  I•',l)])ill^^  West  IJase 

15  j  C()<)])CT 

16  I  Ivp])iii>^  Ivasl  Base 

17  '  IluwanI 

18  i  I'im<)ii 

19  I  MduiiI  Desert 

20  ;  Tunk 


35  5'^  55'i.> 

62  41  3670 

75  I"  3 '■4'^ 

i"5  3"  I ''■^4 

17^  5^  5i\>" 

236  (K,  \ys\ 

3'5  37  5299 


"■32 
.,•36 

"■33 
"■33 
"■33 
"■34 
'"•34 
"34 


(rr«»)  Itt'lft) 

"S^V  5^' 159 

'•'7^  37 -Vv 

ofntif  32<>Sy 

o.Syi  15749 

■•■397  5"  9'J3 

"442  ^^^'^^ 

"■326  533 1^ 


ridliaUlc  ti  ror  (if  a  siiiijlc  oIiscia  aliuii  (  3/).  and  3  A',  int'a  ilireition,  /•,  —    •   it"  .i^i.     Nninl)cr  of  an>;le-. 

adjusti-il,   i.|. 

'I'loik,  llaindi'k   Connly,  .Maine.      ()cl()l)er   27   lo  ()cl<)l)er  31,   iSSy.      25  "'  re|K-aliiix  iheiwlnliu-  No.  \\. 
C.  (  >.  Boulelle.  oliserver. 

0        ()»>        (X'Olt 

67  44  5^53 

•\>  49  3"'54 

I  iS  30  i>.*S"3.s 

144  27  2916 

201         !l        04-45 

275     5*-"     53"'^ 

Probable  error  of  a  sinijle  observation  I  3/^.  ami  3  A'.  1  of  a  ilireclioii,  f-,  =  :»r  I  "'37.     NuinlK.-r  of  ail>;le> 
adjusted,   1 -• 

/'/;,'(■('«,  Wasliinnloii    i.ounl\  ,    Maine.      t)clober    ly   to    25.    I "-"Sy.      25  '"   rciH-atinj;   llic<><it>lile    Ni'.    4^ 
C.  ().   liouteile,  observer. 


21 

I  Inni])liaik 

22 

''•PP'"K  \\'est  Hasi 

23 

ICp])in>i  Ivist  Ba.se 

24 

Hurke 

25 

Pij^eon 

26 

IMonill    Desert 

Sannders 

:o-4S 

O'tJIHI 

(MJ'IJI  I  1 

U-4.S 

0S36 

55 '^94 

o'46 

o'i>7i  1 

3<j'6ii> 

i)-46 

"■'>75 

"7-5"5 

046 

01 54 

293' 4 

"•47 

yV22\ 

l»4'226 

"5' 

27 

Monnl  Desert 

• 

Sannders 

2S 

Tnnk 

29 

Umke 

3" 

llnnijiliaek 

31 

I'lppiii!.;  West  Ikise 

32 

Isppini.;  I'!,isl  It.i.se 

33 

I  loward 

O  IX)  (K>IX) 

45  00  4299 

74  49  "2S6 

90  12  3.S14 

92  09  19-50 

104  56  40-61 

'23  57  37' '7 

1 7h  41  3 1  -69 

Prob.diK-  erior  of  .1  single  obstixiiion  \  3/ '.  ,ind  3  A".  I  of  .1  direction,  f",  =  2:  l".ll.     NuinltiT  of  ;ni)»U-> 

.idjusti'd,   \.\. 


-0-27 

O'OCM 

OO'IKXI 

I)' 29 

0-27 

-0326 

"2-5.U 

'^^■25 

■^^477 

3N-6I7 

026 

0-033 

19467 

0-26 

1-4S2 

42  .*)2 

0-27 

•  0-303 

37  473 

''■25 

•  "5.^6 

-,2   22*1 

32 


THE    EAvSTERN    OBLIQUE    ARC. 


.^/>s/rinis  of  irsii/liiii;   horizontal  directions  olncrvcd  and  adjusted  at  stations  forniinff  t/ie  hase  net, 

/S^6-/S^g — continueil. 

Huiupl)aetc,  Hancock  County,  Maine.     July  19  to  vSepteni?)er  6,  1S5S.     75'"'  direction  theodolite  No.  i. 
A.  D.  Baclie  and  G.  \V.  Dean,  observers. 


Xu.  of 
direc- 
tions. 

Obje 

34 

Cooper 

Azimuth  Mark 

35 

Howard 

36 

Epping  East  Base 

37 

Epping  West  Base 

3S 

Pigeon 

39 

Burke 

40 

Tunk 

41 

Mount  Desert 

Ragged  Mountain 

Saunders 

Mount  Harris 

Resulting    direc- 
tions from  station 
adjustment. 

Approxi- 
mate prob- 
able errors. 

Corrections 
from  base 
net  adjust- 
ment. 

Final 

seconds 

in  trian- 

gulation. 

0 

/ 

'/ 

" 

// 

r/ 

0 

00 

00 -000 

d=0-I50 

OQ-QOO 

39 

37 

40-23 

0-163 

40-403 

39 

45 

46.385 

0-126 

+0-605 

46-990 

59 

43 

io'4oi 

0-136 

+0-1.^,5 

10-536 

69 

3S 

48-051 

0-151 

-^- 0-084 

48 -1 35 

84 

09 

57 '099 

0-125 

—0-223 

56-876 

85 

14 

25-280 

0-142 

— o-o86 

25-195 

102 

22 

1 1  -498 

0-143 

+0-093 

11-591 

114 

33 

50-877 

o'ogo 

+0-779 

51-656 

154 

2S 

20-545 

0-132 



165 

12 

47-118 

0-131 

I. So 

36 

29-988 

0-169 

Number  ( >f  positi(  ins  of  circle,  -V.     Probable  error  of  a  single  observation  of  a  direction ,  <',  = 


■91. 


JMount  Desert,  Hancock  County,  ^Nlaine.     August  14  to  October  14,  1S56.      75' 
No.  I.     A.  D.  Bache  and  G.  \V.  Dean,  observers. 

o  /  //  // 

Isle  an  Haut 


Mount  Harris 
Saunders 
Azimuth  Mark 

42  Humpback 

43  Tunk 


direction  theodolite 


44     I  Burke 


45 
46 
47 


Cooper 

Epping  P<ast  Base 

Howard 


48        Pigeon 

NuniVjer  of  positions  of  circle, -V. 


0 

00 

00  ■  000 

±0-141 

33 

39 

21-332 

0-108 

70 

54 

51-931 

0-121 

93 

48 

58-382 

0-103 

122 

49 

25 ''36 

0-098 

I144 

20 

00-152 

0-078 

O'OOO 

00-000 

•     0 

00 

00-000 

ii53 

19 

24-878 

0-107 

+o-2o6 

24-932 

>     8 

59 

24-726 

fi7i 

09 

49736 

0-148 

-  0-399 

49"iS5 

'-  26 

49 

49'584 

ii75 

20 

34-430 

0-115 

+0-068 

34-346 

'31 

00 

34-278 

1176 

36 

26-634 

0-132 

—0-062 

26-420 

^2 

16 

26-482 

./199 

47 

46-624 

0-132 

+0-756 

47-228 

'55 

■^7 

46-472 

(201 
■  57 

46 

49-121 

O'lIO 

+0-390 

49'358 

26 

48-969 

Probable  error  of  a  single  observati 

on  of  a  direction,  e^,  = 

±o"-86. 

liASK    LINKS    ANIJ    UASl-,    Nl'.TS. 


n 


Alislnjrt\  (if  rr^iiltiiii;  lioii-UDildl  t/inilioNs  iih.un'iit  itiitl  itdjustid  at   sliiti(iii\  f<ir}niu^  the  fui.t-  iifl, 

/S^6-/S';<j — crdiiiiiucil. 

llouHinl,  \V;islnii^;l()n  (.'<innl\,    .M.iinc       July    i ',  lo   August   X,    1S59.      75"'  ilin-ctioii  lliuiylulili-  N'l.    1 
A,   I).   liaclic  .iml  C.   W.   I  Jciii,  oliscrviTS, 


No,  ol 
(lircc- 
lioiis. 


olijccis  iibsdvi-il. 


kcHiilliiiK       'lirec  \\,\,x;xx  /:"',, '.'.'il'        ,     " 

lions  fri.iii  Nl.itioii       irial.- |jri/l.-      „;,.',i„,       :. 
;.,lj„.tn.,nl  ....I..Vror.      "•'„•'''■"■     'L     ■ 


49  I  I'lKfO" 

50  j  Mount  Di'scrl 

51  I  Murkc 

52  '  l'',])])in),;  Ivisl  I'.risi' 

5,^  I  lUMll)l).l(k 

54        Cooper 

A/iiMUth  Mark 
Trescott  Rock 
(iranil  .Maiian 
NunibiT  ol  positions  of  lirclf,  \'.      I'rohahk- t-rror  of  a  sinj^jlc  observation  of  a  ■lircclioii,  »,    =       i"  ly. 

Coof>t)\  \V'asliin),;l<)n   Couiilx  ,    Maine.      Auj^usl   30  lo    Septenit)er    16,    1*^59.      75  '"   ilirection    the'xloliti- 
No.   I.      .\.   1).   Hailu-  .1111!  ('..  W.  Dean,  observers. 


ilirin 

"  •• 

'■ 

/ 

// 

" 

" 

// 

ft 

(X) 

H,l*t, 

■  01.10 

0  <</) 

•  n  i>r 

1 

'9 

25  944 

"■'77 

'1    1  12 

iS^\2 

22 

<'2 

\\\iU 

0  21  •, 

o-.^S 

^•'5"' 

.5.^ 

,v> 

40- 141 

0  191 

0204 

1"  V45 

5' 

•Vl 

41-50.5 

"-'73 

•    1    231 

;2  7^'i 

|(..S 

01 

.'7  996 

oil  1 

o'o22 

2^'o: '' 

'23 

5' 

19  227 

'1      MM 

19  21/. 

:73 

43 

51-973 

0    IC^I 

1S9 

2S 

45-^43 

0161 

Cliaincook 

I'rinee  Regents  Ri'ilonbt 
C.rand  Manan 
Tii'seott  l\ot'k 


0  (K)  00000 

.VS  36  49-O.S2 

54  40  14-493 

6S  43  51-6.S7 

I   loS  5^5  1K)3,S5 

I         (1  00  (H)'l»«) 

I '57  47  '"'-7'^; 

\   4S  50  5" 'I'M 

160  II  .10754 

1   5 1  15  ;,  I  ■369 

I  192  12  4301.1 

I     S3  16  33 -^21) 

294  13  (vS-,S,)4 

I1S5  \c  39-.IU) 

Nninlierof  posilionsof  eircie,  \'.      I'robaliU- errorof  a  simple  observationof  ailireclimi.  c,  =:t  l"li). 


Ilowar.i 
Mounl  Desert 
lUnke 
Ilunipltaek 
.\/iiniitli  .Mark 


01 17 

0  197 

0  23S 

0  161 

"  133 

iroiitt 

1 1  >'i  ■  ■  • 

OIS.S 

0-641 

52  •■45 

"149 

"57'^ 

3 1  94"^ 

I" 


'5^7         33  "42 


.59-57: 


I'li'iMNT.  H.VSI-;  Niri'  .vi>ji  s'i"mi-:nt. 

( Vi.s(7-r<f/;()//  ,i/itiifti>iis. 

1      0=  t  217S07  I  0-40133^5)     o37S95(^4)  ,  o•hU194^32^    1  •53''^5i^(  3 '  i  •  >'-Si3o2i  3; 

-2(>i(x.7(37)  i  1-20305(36)     002237(7)  (0-92756(30) 
II     0=  10-283  I  (S)-  (12)  ,  (37)     (36)  •  (5)     (4) 

III  0=     0-698  t-(32)     l3'-'Vf(3>^^     (36)  :  (5)     (7) 

IV  0=     o-8ti7f(3i)     t3o)+-(38)     I37)l-(ja)     (9^ 

V     0=     6.125S8  ;  o-8tx)64(3i)     5-3l^)l>S^  24)  •  10-47161(39)     ii-2:6«.\ji  38)     6-J»xi62t3o^ 

'  ^''754431,37^     0-167821  12)     o;o2i2i  10)  •  o-46<.k>.|i  o) 
4U)J      Xo.  7 — 02 .^ 


34 


THE    EASTERN    OHI.IOUE    ARC, 


VI  ! 

o= 

VII 

o= 

VIII 

o= 

IX 

o  = 

X 

o^ 

XI 

o= 

XII 

o= 

XIII 

o= 

XIV 

o= 

XV 

o= 

XVI 

o= 

XVII 

o= 

XVIII 

o^ 

XIX 

o= 

XX 

0  = 

XXI 

o= 

XXII 

0= 

XXIII 

0= 

XXIV 

0= 

XXV 

0= 

XXVI 

0= 

XXVII 

0= 

XXVIII 

0= 

XXIX 

0= 

XXX 

0= 

XXXI 

0= 

XXXII 

0= 

XXXIII 

0= 

XXXIV 

0= 

XXXV 

0= 

[The 

log- 

Ohsei'z'afion  I'qiialioiis — continueil. 

:  +  r292-^(io)-(9)  +  (3i)-(29)  +  (iS)-(t4) 
:-|-o-768-r(  [S)-(  i3)^(39)-(3S)  +  (3o)  -(29) 

=  +o-o84S3-ro-257oo(i6)-o-54S4i(i4)  rO-29i4i(  i3)+o75443(39)-i'9574S{37) 
-1-1-20305(36)     0-40132(5  )  -;  o-i6676(  2)  -0-56808(4) 
-o-7S8-j-(i6)-  (i3)^-(39)    -(36)+(5)  -(2) 

-I -34263-0- 182841  II)   -o'65278(  10) -1-0-46994(9) +0-80064(3 1 )  — I '56540(29) 
i  o-76476(  28  )  -r-o-43254(  25  )  -  -o-6o454(  24)  -|-o-  i720o(  22  ) 
-2-555-:  (20)- (18) -K  (29) -(28)  I- (25) -(24) 
-r726+(25)-(22)  +  ([i)~(9)-f(3i)-(28) 

:— 0-6877  1-^0-3  151  2  (32) --1-07988(29) -1-0-76476(28)  -(-0-43254(25)— 0-73688(24) 
-0-30434(23) -1-0-43596(3)— 0-65063(2)    +-0-21467(7) 

-o-929^-(i6)-(2o)^(24)-(23)  +  (3)  -(2) 

- 1 '58338-  0-73062(23  ) -0-81676(22 ) +0-08614(21  )-|-o-32768(  40) -I -53073(37) 
+ 1  ■20305(  36) -ho-4oi32(  5 )  — o-836o6(  4)  4-0-434741  3 ) 

+  0-I53-(40)-(37)^(l2)-(ll)+(22)-(2l) 

+0-22432  ^o-65422(  44 )  - 1  -98508(43 )  -f  T  -33086(42)  ^o-97432,(  41 )  - 1  -65748(  40) 
-1-0-683 16(  39 )  -  o-2i525(  13 )  -o-25436(  20) -f  0-0391 1(19) 

-o-907  +  (i3)  --(i9)  +  (44)-(42)  +  (4i)-(39) 

-i-ii7-(4i)-(4o)  +  (2i)-(26)  +  (43)-(42) 

- 1 -832i8  +  2-20947(46)-2-62575(44)-Lo-4i62S(42)^o-374S4(4i  1-0-81586(39) 

-)-o-44io2(36)-fo-03977(5)-o-9ri52(2)J-o-87i75(i) 

-i-27i  +  (2)-(i)  +  (46)-(44)-^(i9)-(i6) 
=  -0-44146^0-67443  (30) -0-73 156(28) +0-057 13(27) +0-18656(48) -I -51742(43) 
-hi'33o86(42)  +  o-97432(4i) -1-61457(40) +0-64025(38) 

-i'35S  +  (3o)-(27)  +  (48)-(42)  +  (4i)-(38) 

+0-92970  fo-44io2( 39) -I -02088(36) -1-0-57986(35) +0.66575  (53) -I -70358(52) 

+  I'o3783(5i)+o-3599o(i7)-o-4i562(i6)+o.o5572(i3) 
=  +  o-303^(2)-(6)+(52)-(5i)  +  (i7)~(i6) 
-o-i34+(36)-(35)  +  (53)-(52)  +  (6)-(5) 
-I -36912^-0-66575(53)- 1  ■ooo27(  52) +o-33452(  50) +o-49i53(47)-o-82493(  46) 

+o-3334o( 42 )  +0- 14829( 4 1 )  -0-72815(36 )  +0-579861  35 ) 
=  -r7i6+(i)-(6)^(52)-(5o)H-(47)-(46) 
=  +o'5 1527  fo'3589o(4i) -0-57388(38) -0-214981 35  )+o- 17014(53  )+S-94070(  49) 

—9-1  io84(  50 )  +5-94358(48 )  -6-07800(47 )  -ho- 13442(  42 ) 

=  -o-o56+(33)-(27)  +  (48)-(47)  +  (5o)-(49) 

=  -i'75954+o.33673(58)-5-337i9(57)+5-ooo46(56) +2-88157(45) -3-29785(44 

+o-4i628(42)+o-37484(4i) -0-39237(39  )-!-o-oi753(34) 
=  +  1-216  f(i9)-(i5)  +  (57)-(56)  +  (45)-(44) 
=  +o'38o+(4i)-(34)  +  (58)-(56)  +  (45)-(42) 
=  +o-822i7+4-83i53(57) -5-00046(56) -^o-i6893(55)+o-oi479(54)-o-57i45{5i 

+o-55666(5o)+o-38566(47) +2-49591(44) -2-88157(45) 
=  -r463  +  (47)"-(45)  +  (56)-(55)-|-(54)-(5o) 
differences  for  i''  are  given  in  units  of  the  fifth  place  of  decimals.] 


I'.ASJ-.    IJXI-.S    AM)    l;ASI'.    Nl-.TS. 


Tile  ic<i|in)(;ils  of  llic  we-i^^lils   iiitrodiu cd    lor  Uk-  ^e\'Lr;il  (lircLti<Jii'>  ari.  a>  tollow-. 


nil 

,     1  /. 

iiii 

'  /' 

iiii ' . 

1  /■ 

I<n 

/' 

l»u    • 

^/' 

iJlr 

1 

()■  I()2 

1  1 

o-r„S4 

21 

"■2.59 

(  max. 

.il 

009S 

41 

i,-o3S 

5' 

2 

o-foS 

1  2 

o-o,S7 

22 

0-256 

.^2 

0102 

1-' 

0  0^6  1  mi 

1    1     5-' 

?, 

OKJ.S 

i;^ 

"1.^2 

2,; 

"■2.W 

,v> 

0.094 

43 

..012 

5  ^ 

4 

<ri2S 

'1 

"•'57 

2| 

o-2|l 

34 

"■"53 

44 

0052 

5J 

5 

(1 '  1  ( iS 

15 

.i-l.vS 

2.S 

"■2,^<> 

.35 

00 16 

45 

0-041 

51 

(> 

W  1  Id 

i6 

"■'.V; 

26 

"■2.V' 

:i'> 

""19 

V' 

.. ■,.,■•, 

S6 

7 

D'l  12 

'7 

o-ip 

-7 

" ' '  "5 

37 

"■"53 

17 

....JS 

57 

s 

((■()6,s 

I.S 

,.-||.S 

2.S 

o-lol 

:>^ 

.,-o|'> 

4^ 

M-.,,J 

5^^ 

9 

oviyo 

'9 

"I'll 

29 

"■"91 

39 

"■".5" 

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"■"5' ' 

III 

"''>9.i 

211 

.ii,K, 

^" 

II  (KjS 

-1" 

DOS  1 

5" 

0-</>2 

TliL-  corrclaU-  and  iiomial  eijuatioii.s  iiia>'  l)f  t<>mul  in  Coast  Stir\-L->    kL-]»<jrt  lor  i.s'u. 
pp.    I  ,iJ-i36,--'  tliL-  rL-sulliu};  corrL-ctions  to  tin.-  .sc-\-c-ral  direction-^  arc  a-  follow- 


(11  = 

(2) 

(31 
•(41 

(5) 
(61 

(7) 

(«) 

(9» 

(  III) 


=    i  "■a  13 

1  1  II 

"■,V|.' 

(211     - 

o-2.Sl 

13'  1 

"■343 

(  121 

"■33' 

(221 

"■555 

( 32  > 

i:.\s 

1  131 

(1-1  17 

(231 

"■351 

1331 

"■26;, 

1  14) 

•    0-412 

(  2-1  1 

"594 

134) 

:   "■<)56 

(  '5' 

1  1  i(S  1 

1  25 

"■435 

'  35  1 

ir;,6y 

ti6i 

"■49-' 

I  26  1 

"■".57 

136.1 

11-66.S 

(  171 

1  -(Kl.S 

'-'7 

"357 

'37' 

(1-22(1 

(  iSi 

"■514 

(  2.S  1 

"■6S3 

1  3.S  1 

"•731 

(  19  • 

"■559 

(291 

o-  1  21 P 

1  39 ' 

(1-6.1' 

(  20  ) 

(1'2(19 

(3"i 

"39" 

(.}ni 

l-'or  i-lu-ck  1 

wi-  lia\i- 

:;•(/..-:■ 

1     ■    •    1 

7 1  3 1 

:itiil 

|.v  C 

•    1 

7'14- 

I  •  1 25  1411 

"■"54  142- 

0-179  '4>i 

0-196  (44 

"•4"9  145' 

0.061  (  46  i 

0112  I  47 

0.419  i.\S. 

0-2S2  I  49  ' 

i>-  In;  I  5. 


"'43  '52 
..063  (5;, 
"5  12      I  54 


■613 
247 


'iMu-    jiriiiialiU-    error    ol     .1    diri.-i-lion   of    iiiiil.    U(.-ii;lu     is    tlicrcfon.-    "■"74  ./'-'' 

('■(i;  1   ./    '     ■■*        -I    I ".  p). 

'Plu-  ri-tMpr(>(.'al  of  tlu-  a\L-ia.!4(.-  wt-ii^lil  of  a  direction,  or  1  /-  fi|naU  .iimi,  hciict-  tlic 
prolialiK-  (.rror  of   an  ol>s(.-r\-t-d    dii\-clion  (.-([nals  1  41)    .'  r    ■      .j"     and     that    of     .1:1 

aiii^li-    I-  i>".('7. 


r.iuk(- 

l-!]ipiii.i;  West  lia.si- 

I'^ipiiiv^  I'!. 1st   Base 

■riMils 

l-^ppilii;  Wr.st   Ua.-ic 

I'!p]>iii,v;  Ivisl  li.i.-.!.- 


Ol>-.il\<il  .llli;li-~ 

M)  ii-)  35  '^S" 

Si)  03  11  -750 

51  37  12  -gixi 

111  <i|  3-1   oio 

13,^  ,.|  37    ,i.S.. 

.'.^  31  ■  .M-.S|>> 


C.illn 
lioM 

ical 
atiijU- 

Sphi-r 
"u-al 

11  -(VS.. 

35    93" ' 

11   \>~<.) 

0-422 

1  1    32S 

.1  -ivSi 

■  0  -ivS»i 

I2-9S.. 

"  'IV-) 

1 1  -gi l^  3.J  -9 \h  o  -vVvS 
n  ■  I  22  3ti  -g^sS  n  -1167 
I    31  I       iS  -329     o  •06S 


*  With  chim.nvd  imtutidii.  llu-  i>rcsciit  one  lii-ini;  111. nc  c\>tiveniciit  for  i>rinliiii;  ;i~ 
I  U  is  not  iiuitt-  cx.u-t,  I'oi-  llu-  ri-asoii  lliat  :iflfi  llu-  ni-iu-r.il  liutirc  ;>iljii-tmrnt  h 

the  I'oii-fclions  to  tile  ilim-lions  wt-ii- not  :issni-i-«l  .in>l   h:ul  to  In- fiirtlu  • 

lidol'  tlinl  rciiort  coiit-l.ilf  xwi  for  -vhm;  n-ail  .;.|.».l; 
I  I'lililishid  in  I'oasi  Shim  \    Ki  i>oil  fot   iV<.,.  ji). 


I.01!  .lis 
lam-cs 


3  -iM-i  314  34 

4  i3'^'  343  '■'4 
.|  ■032  670  7s 

3  i>4o  314  34 

4  322  77^  '^• 
4   I3-3JS 


S  715   «^»4  2 
13  751     .Vi^ 


r 


36 


THE    EASTERN    OBLIQUE    ARC. 


No. 


13 


14 


Re^ulinii^ 

angles  and 

S7(/(-.V  <)/"// 

w  Epping 

basi'  net 

,  jMainc 

— continuea. 

stations. 

Ob 

0 

serve 
/ 

d  angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
e.xcess. 

l,og.  di.s- 
tances. 

Di.stances  m 
meters. 

Tunk 

50 

45 

II  -850 

-0  -039 

II  -811 

0  -094 

4  -032  670  78 

10  781  -291 

Epping  West  Base 

49 

01 

45  -330 

+0-300 

45  -630 

0-094 

4-021  662  33 

10511  -443 

Burke 

80 

13 

02  -640 

+  0  -203 

02  -843 

0  -095 

4-137  32.S  24 

13  719 -'83 

Tunk 

34 

40 

37  '840 

-0  -945 

36  -895 

0  -106 

4-13S343  64 

13  751  -296 

Epping  East  Base 

25 

46 

43  '060 

+  1  -591 

44  -651 

0  -106 

4  -021  662  33 

10  511  -443 

Burke 

]i9 

32 

38  -490 

+0  -283 

3S  -773 

0  -107 

4-322  77S  80 

21  027  -072 

Pigeon 

19 

00 

56  '560 

—  I  -180 

55  -sSo 

0-17S 

3  -940  314  34 

8  715-942 

Epping  West  Ba,se 

64 

55 

oS  '300 

+  0-951 

09-251 

0-178 

4  -384  324  57 

24  228  -391 

Epping  East  Base 

96 

03 

55  '500 

+  0  -402 

55  -902 

0-177 

4  -424  896  92 

26  600  -936 

Pigeon 

33 

44 

59  '030 

-0-174 

58  -856 

0-197 

4-138343  64 

13  751  -296 

Burke 

lOI 

48 

19  -820 

-  I  -005 

18-815 

0-197 

4  -384  324  56 

24  228  -390 

Epping  East  Base 

44 

26 

42  -600 

+0-322 

42  -922 

0-198 

4  -238  S47  61 

17  331  -957 

Pigeon 

49 

oS 

34-310 

+  0  -629 

34  -939 

0  -405 

4  -322  778  80 

21  027  -072 

Tunk 

60 

37 

58  -620 

+  0  "084 

58  -704 

0-405 

4  -384  324  57 

24  228  -391 

Epping  East  Base 

70 

13 

25  -660 

+  1-913 

27  -573 

0  -406 

4-417  660  18 

26  161  -352 

Pigeon 

14 

44 

02  -470 

+  1  -006 

03  -476 

0  -099 

4  -032  670  78 

10  7S1  -291 

Burke 

141 

07 

55  '670 

-0  -925 

54  -745 

0  -100 

4  -424  896  91 

26  600  -936 

Epping  West  Ba.se 

24 

oS 

03.  450 

-I  -373 

02  -077 

0  -099 

4  -238  847  61 

'7  331  -957 

Pigeon 

30 

07 

37  750 

+  1  -809 

39  '559 

0-295 

4-137  328  24 

13  719-JS3 

Tunk 

76 

42 

32  -630 

+  0  -990 

33  -620 

0-296 

4  -424  896  91 

26  600  -936 

Epping  We.st  Base 

73 

09 

48  780 

-I  -073 

47  -707 

0  -295 

4  -417  660  18 

26  161  -352 

Pigeon 

15 

23 

35  '280 

+  0-803 

36  -083 

0-  lOI 

4-021  662  33 

10  511  -443 

Tunk 

25 

57 

20  780 

+  1  -029 

21  -809 

0-102 

4  -23S  847  61 

17  331  -957 

Burke 

138 

39 

01  '690 

+  0  -723 

02  -413 

0  -102 

4  -417  660  18 

26  161  -352 

Humpback 

9 

55 

37  '650 

—  0-051 

37-599 

0-105 

3-94031434 

8  715  -942 

P^jping  East  Base 

27 

41 

01    TJIO 

+  0  -320 

01  -330 

0  -106 

4  -370  860  02 

23  48S  -756 

Popping  West  Base 

142 

23 

2  J    -940 

-0  -551 

21  -389 

0  -106 

4  -489  329  42 

.30  S55  -275 

Humpback 

25 

31 

14  -879 

—  0  -220 

14  -659 

0-352 

4-138  343  64 

13  751  -296 

Epping  East  Ba.se 

79 

x8 

13  -910 

—  0  -400 

14-310 

0  -352 

4  -496  419  39 

31  363  -129 

Burke 

75 

10 

31-480 

+  0  -609 

32  -089 

o'353 

4  -489  329  43 

30  855  -276 

Humpback 

42 

39 

01   -097 

-0  -042 

01  -055 

0-441 

4  -322  77S  80 

21  027  -072 

Epping  East  Base 

53 

31 

30  -850 

—  I  -192 

29  -658 

0-441 

4-397  174  17 

24  955  -954 

Tunk 

S3 

49 

3"  '540 

-}  0  -070 

30  -610 

0-441 

4  -489  329  43 

30  S55  -276 

Humpback 

24 

26 

46  -698 

—  0  -358 

46  -340 

0-525 

4  -384  324  57 

24  228  -391 

P^pi-iing  East  Base 

123 

44 

56-510 

+  0-721 

57-23' 

0-525 

4  -687  346  90 

48  679  -590 

Pigeon 

31 

48 

17  '670 

+0  '335 

18  -005 

0  -526 

4  -489  329  42 

30  S55  -275 

1,1 


iS 


19 


15. 

ksi-: 

IJXlvS 

AND    1 

5ASK    NKTS. 

37 

k;-., 

llini^ 

(lllL'Ji^ 

iii(t 

k/i-s  III  till-   /■.f>f>IIIL, 

fnisi-  Hi- 

/,  Maine — coiiliiiueil. 

Slrilioiis. 

01. 

0 

iirvi-( 
/ 

1  .iIIKlrs 
// 

Correi 
lion. 

ical 
aiiKlt--.. 

S|»htr- 

ical 
rxec-,.. 

!.'-«    .11-. 
laiicr.. 

I  Iiiiii]jli.i(k 

'5 

35 

37  229 

..•i6<^ 

37-</y, 

0  ■  1 67 

I 

032  670  7S 

10    7SI 

291 

I'',])|iiiij4  \\'r^t   15 

-ISC 

12K 

33 

26  Viio 

:  "  '973 

27  -28;^ 

(.■16H 

4 

49^41939 

Ji  3^^ 

129 

I'.inkr 

?,S 

5" 

55  '^3" 

'>'529 

5^'    •59 

0    167 

4 

-370.S600-, 

23  4HS 

7S7 

1 1  iiiii{ili.u'k 

32 

43 

23  -447 

0  '(XK) 

23  45^ 

'.■26.S 

4 

137   V8  24 

'3  7'9 

02 

IvjiliiuK  \Vrsl   I! 

'ISC 

7<> 

31 

40 -yK*. 

• "  ■^>74 

4'  '^^St 

'.  ■26.S 

4 

•397  '74  '7 

21  9SS 

9S» 

•I'liiik 

^>7 

11 

5^'  ■530 

(.■S;/) 

55  694 

o-26.S 

I 

-370  .S6.J03 

23  4^*^ 

757 

1 1  min)l>;u'k 

'  1 

3' 

rKj  •()  |.S 

"  'y>^ 

().S74<. 

<.-242 

4 

424  896  91 

26  6r«. 

956 

r'lipin.H  West  15 

ase 

'5-' 

41 

29  •760 

"■399 

29-361 

0-242 

4 

'^1  34^9' 

4S  679 

5</' 

l"i};.-nii 

12 

47 

21     IK) 

I  ■515 

22  625 

..■241 

I 

-37r,  S6004 

23  4HS 

■757 

1  Iuiu|)l)ack 

'7 

07 

46 '2  18 

..•i7,S 

4^>  396 

"■•95 

4 

021  662  33 

10  511 

443 

liiirkf 

44 

22 

07  'OIO 

()-326 

(16  -6X4 

"■'95 

4 

■',97   174   IS 

24955 

"954 

'I'unk 

iiS 

3'> 

oS  -^So 

'••■S75 

07  '5"5 

"■'95 

I 

496  419  40 

3'  3'>i 

'3" 

I  Iuin]il>,u-k 

I 

04 

2S|,S( 

'  "^''Lv^ 

28-319 

I)  -024 

4 

-23.S.S47  '" 

'  7  33 1 

957 

PiK'roii 

1 

5''' 

41    ^^o 

"■5"9 

40 -.S5. 

0  •024 

4 

•496  (19  39 

3'  363 

124 

liuiki.- 

176 

5'^ 

5'  W"' 

-"■397 

5"9f'3 

0-025 

4 

-6S7  346  9 1 

4S  679 

■5V 

1  Iiun])li;iok 

IS 

12 

14  399 

■  ' '  '3 '  ^' 

i4  7'5 

0  -321 

4 

417  660  IS 

26  161 

352 

riKccMi 

'7 

20 

16  ■640 

•  "  293 

■''■933 

0  320 

4 

■397  '74  '8 

24  955 

■954 

'I'liiik 

144 

27 

29  ■|6() 

!  fi54 

29-314 

( >  '\2\ 

4 

-6S7  346  91 

4S  679 

■590 

Mount   I)rS(.-rl 

5 

26 

36  -.SgS 

f  "  "337 

37   235 

0-129 

4 

'3''  343  ^^4 

'3  75' 

-296 

r.iirki- 

160 

5« 

42  ■36" 

1   051 

41  -31 H^ 

0  - 1 29 

4 

■674  354  i" 

47  244 

■■9'^ 

I'.ppiiiL;  l'",;ist  I!,- 

sc 

'3 

34 

42  -.(ex. 

"■557 

1 1   843 

0  - 1 29 

4 

-531  S7S92 

34031 

3-^'  * 

.Miuiiil   IH-si'il 

-3 

'7 

01  756 

0  ■26.S 

01  -4S,s 

"■532 

4 

•322  77'^  •'^^ 

21  027 

■••72 

'I'uiik 

'17 

21 

33  '9'" 

0  294 

33-616 

"'533 

4 

-674  354  ... 

47  24- J 

■79'> 

Mpliini;  Ivisl  B: 

sc 

39 

21 

25  MSo 

■  1  •»3  4 

26  -494 

' '  533 

4 

-52S  .*s  3^1 

33  733 

•.V.7 

Mount  Dc-scrl 

25 

10 

22  -4X7 

\  i>  45 " 

22  -938 

..•496 

4 

>'^4  325  57 

24  22s 

3m 

lvi)piiiK  Iv'sl  Kasi- 

3" 

52 

CX)  •20() 

1  0  •S7S 

m  -078 

0-496 

4 

'4'^5  73'  76 

29  223 

■4'>'' 

Pivji'ou 

'23 

57 

37   170 

1  i»\V>3 

37  "473 

0-497 

-i 

-674  354  ... 

47  244 

T-^"^ 

Mount  lk-S(.-rl 

32 

1(1 

26  •4S2 

u  '1)62 

2(1  •420 

1    231 

4S.)  32.)  43 

30  855 

27'^ 

lhuii|)1)ai-k 

54 

5*' 

40  476 

t  0  -hi;. 

41     lU) 

1    23  1 

•'■'74  354  '•• 

47  244 

T"-*" 

I'lppiuL;  Ivast  \\\ 

sc 

92 

52 

5'>'3ii' 

"■"57 

5''  153 

1  -230 

761  26S  03 

57  7»2 

253 

Momil    Drsi-il 

'7 

5'> 

24-S5S 

0  ^ii.S 

24  253 

0-297 

-021  6f>2  33 

u>  51 1 

443 

'I'mik 

Sj 

4>' 

56  070 

■  0  '65  1 

5''  721 

0  -29: 

53 '  ■'^7^  93 

34  031 

■33-^^ 

llnik> 

79 

jS 

39   "50 

I  I)  •76,S 

39  '9 1  >> 

o-2v)S 

-52S  .<)5  3ti 

33  733 

•S07 

Mount   DosiTl 

3" 

3'' 

59  w^s 

;  0  •7SS 

60  -173 

0-42S 

-23S  S47  M 

'7  33" 

957 

I'.uikr 

59 

10 

22  •54(^ 

0  1145 

i^  495 

0-42S 

■4*^5  731  ~'^ 

2^)  223 

\f^^ 

rii;<.'oti 

i)<) 

1  2 

;,S-i4>' 

0  470 

3S  -b  1  (> 

0-42S 

-531  S:s  g." 

34  03 1 

-vV* 

3S 


THE    EASTERN    OBLIQUE    ARC. 


28 


29 


n 


34 


35 


36 


37 


3« 


/\esnlli>!g  aiiiiU's  and  sides  of  the  lipping 

Correc- 


basc  uii ,  Maine — continued. 


iNIount  Desert 

Humpback 

Burke 

Mount  Desert 

Tunk 

Pigeon 

Mount  Desert 

Humpback 

Tunk 

Mount  ]  )esert 

Humpback 

Pigeon 

Howard 

Burke 

Epping  East  Base 

Howard 

Pigeon 

Epping  Blast  Base 

Howard 

Pipping  East  Base 

Humpback 

Howard 
Mount  Desert 
Pipping  East  Base 

Howard 

Pigeon 

Burke 

Howard 

P.urke 

Humpback 

Ho  want 
Mount  Desert 
Burke 

Howard 

Pigeon 

Humpback 


( )bscrvcd  ansrles. 


26   49 
123 


48 
56 

74 


19 

27 
43 


49  02 


8 
12 


59  24 

"  39 

I5«  48  55 

26  48 

23  53 

''9  19 

28  06 

19  45 


57 
30 
92 
1 1 
30 
I3<S 


•5S4 
•597 
•160 

•243 
•2yo 
■S60 

■726 

■379 
•550 

•969 
778 
■500 

■005 
r6o 


1 2  09  '940 


33 


52  43 
93  45 


30  40 
54 

27 


17 
142 


29 


'9  57 


32 
23 


1 24  37 


86 
71 


28 
28 


01 
36 
24 

14 
'9 

27 

34 
53 
34 


29  or 
105  30 
45 


07 
30  16 

28  38 


20  43  08 

28  37  56 

130  3S  57 

5i  03  41 

84  32  12 

44  24  10 


•141 
•520 
■340 

•364 
•150 
016 

■197 
•990 
•540 
126 
■550 
■660 

•379 
■640 

•S95 
■182 
■888 

•20C5 

■505 
•190 

•714 


-o  '399 
-Ho  -864 
+0  -442 

+0  -183 
-o  -378 
-o  -327 

+0  '206 
-^o  -686 
^0-225 

T-o  -389 

+  1   '002 

-o  -033 

+  1  -171 
—  1  "500 
+  0  '026 

+0  -204 
+0  -233 

— o  '297 

+  1  -028 

-o  -424 
-o  -470 

+0-316 

+o-8i8 
+0  -582 

— o  '968 

+0  -059 
+0  -494 

+  2  -199 

— o  ■891 
— o  '690 

-o  -856 
+  1  '155 
+0  -449 

+  1  '231 
+0  -569 
— G  -828 


Spher- 
ical 


49 '185 

26  ■461 
46  '602 

24  -426 
34-912 
02  -533 


Spher- 
ical 


o  -749 
o  -750 
o  -749 

o  '624 
o  -624 
o  -623 


49  '358 
54  780 
19-467 

07  -186 
43  '660 
09  -966 

40  -345 
54  753 

27  -043 
02  -392 
35  726 
23  '546 

14  ■513 
20  '808 

28  -J 22 

33"i5S 
53  '609 
35  '154 

09  -578 

15  749 
38  -205 

07  -326 
58  -043 
57  '649 
42  -736 
'  2  '759 
09  -886 


1  -202 

I    '202 

I  -201 

o  -271 
o  -271 
o  -270 

0-714 
0-714 
0-713 

0.555 

o  554 

0  -555 
1-148 
1-148 

1  -147 

o  640 
o  -641 

0  -640 

1  -177 

1-178 
I  -177 

1  ■fx)6 
I  -006 
J  -006 

I  794 
'  793 
1  794 


Log  dis- 
tances. 


4-496419  39 

4  ■531  ■'^78  92 
4-761   268  03 

4-417  660  1 8 
4 '465  731  76 
4  '528  065  36 


24-932   0-257 

4-397  174  iS 

40  -065    0-257 

4  -528  065  36 

55  775     0  '258 

4-761  268  03 

4  '687  346  91 
4  "465  731  76 
4  -761  268  03 

4-138  343  64 

4-543  I '7  55 
4  -663  658  76 

4  '384  324  56 
4 '543  117  54 
4  '641  374  53 

4  -489  329  43 
4  794  490  45 
4543  "7  54 

4  '674  354  00 
4  '543  1 1 7  54 
4  -863  228  98 

4-23884761 
4  -663  658  75 
4  '641  374  53 

4 '496  419  39 
4  794  490  46 
4  -663  658  76 

4  '53 1  87>-'  92 
4  '663  658  76 
4  -863  228  98 

4  '687  346  91 
4  -794  490  44 
4  '641  374  53 


Distance  in 
meters. 


31  363  -129 
34  03 1  -330 
57  712  -253 

26  161  -352 
29  223  -468 
33  733  •■'^07 

24  955  '954 

33  733  '807 
57  712  -253 

48  679  -590 

29  223  -468 
57  712-253 

13  751  '296 

34  923  -483 

46  095  -524 

24  228  -390 
34  923  -482 
43  789  '958 

30  855  -276 
62  300  -345 
34  923  '482 

47  244  798 
34  923  -4S2 

72  984  -221 

17  331  '957 
46  095  -523 

43  789  '958 

31  363-129 
62  300  -346 
46  095  -524 

34  03 1  -330 
46  095  -524 
72  984  -221 

48  679  -590 
62  300.  345 
43  789  '958 


No. 


39 


4' 


42 


43 


44 


45 


46 


I'.ASl',    IJNES    AND    JJASK    Nl-.TS. 

A't's/{/////i;  (r//L;//s  lu/i/  M'(/ts  nf  Ihc  /■'.ppiin;  /nise  iii-/ ,  Maim — roiilimicfl 
itioiis  ObsL-rvcd  Miii^lcs. 


39 


t_<jrrer- 
tion. 


S])hcr- 
ical 


Spher- 
ical 


Howar.l 
I'igfdii 
Mount   Deser 

Howar.l 
Mounl  I  )f.sert 
Ilnmphack 

Cooper 

Burke 

Hinii])l)ack 

Cooper 

Mount  Desert 
Burke 

Cooper 

Howard 

Burke 

Cooper 
Mount  Desert 
Humpback 

Cot)i)er 

Howanl 

Humpback 

Cooper 
Howanl 
Mount  Desert 


176 


'  9  25  '944 
41  31  '69(3 
59     02  -497 


;inj;les.       i;xcc-ss. 

0  M  I  2      25  '832  O  '062 

"  '535     32  -225  o  063 

o  -367      02  '130  O  •f)62 


tances. 


49  44  15  '561  !  I  '344  'f''9"5  2  -933 
55  27  46  -472  I  -I  o  756  47  -228  2  -933 
74     48     04-492       I  0-174     04-666     2-933 


32  <x)  62  -260 
62  44  36  -700 
^5      '4     25-280 


—  I  -165  61  -095  I  -389 

+  1-178  37-878  !  -389 

—0-085  25  -195  1  -390 

2     24     39 '965  i   —0-063  39 '902  0-194 

4      10     44 -694  j  +0 -467  45 '161  0-195 

173     24     37-140       -:-62o  35-520  0-194 

51      15     31  '369         0-578  31-947  1-559 

■\S     5-'^     53 ''^^70       to -990  54-860  1-560 

42     45     39 '940       -2-069  37 '871  ''559 

34     25     42-225          1-228  40-997  2-333 

31     (X5     34 -27S       f  0-069  34  347  2-333 

114     33     50 -877  '     ;  0 -779  51-656  2-334 

•\i      "6     33 '629  I       0-587  33-042  1-772 

1  -771 
I  -111 


56     57     46-491   ■   —1-209     45  ■2S2 
3c,     45     46-385      -i-0-605     46-990 


48     50     51-404      +0-641     52-045 
106     41     62-052  I   +0-134     62-186 

24     : 


2  -371 
2  -37 1 


:2-i94  I    f  o -688     12-882     2-371 
ncacriplioin  of  s/alioiis. 


4  '663  658  76 
4  770  5o<S  08 
4  603  402  14 

4 -761  26S  03 
4-720893  21 
4 -967  744  25 

4  794  49^1  46 
4-720893  21 
4  -603  402  14 

4  863  22S  98 
4  967  744  25 
4  -603  402  14 


IJistanccs  111 
meters. 


4  465  731  76  29  223-46S 

4  863  228  98  72  9S4  -221 

4  -641  374  53  43  789-958 

4  761  26803  57  712-253 

4  -794  490  45  62  300  345 

4  -863  228  98  72  984  -221 

4-49641939  3'  363-129 

4  -720  893  20  52  58S  -793 

4  -770  50S  08  58  953  -295 

4-53187892  3403' '330 

4  -770  508  08  58  953  -295 

4-96774425  92841-949 


46  095  -524 

58  953  '295 
40  1 23  -S08 

57  712-253 
52  5S3  -794 
92  84 1   949 

62  300  -346 

52588-79  + 
40  1 23  -SoS 

72  9S4-221 
92  841  -949 
40  123  SoS 


lippiiiij  East  Base. — The  station  is  in  Washinijton  Coitnty,  Maine,  at  an  angle  in 
the  road  from  Epping  village  to  Cohtnibia,  and  directly  npon  the  edge  of  the  escarjv 
ment  of  the  Epping  Plains. 

The  subsiir/acc  mark  is  the  intersection  of  cro.ss  lines  on  a  copper  tiolt  in  granite 
block  2  feet  long,  set  3-5  feet  below  the  surface  of  the  groiuid.  A  platform  of  concrete 
a])ont  5  feet  square  and  i  foot  thick  was  prepared  above  this,  witli  an  opening  in  the 
center,  throtigh  which  the  subsurface  mark  could  be  seen.  This  formed  the  foundation 
for  the  surface  mark,  a  large  granite  l)lock,  3  feet  .square,  carefully  dre.s.sed,  and,  when 
in  place,  projecting  about  6  inches  above  the  .surface  of  the  grotuid,  with  a  copper  lx)lt 
and  cross  lines  in  its  center.  Upon  this  was  placed  a  moniunent  of  marble  y2S  feet 
high  and  1-64  feet  .square,  resting  upon  three  feet,  each  about  3  inches  in  diameter  and 
I  inch  high.  The  in.scriptions  on  the  sides  are  as  follow.s:  north  face,  ""U.  S.  Coast 
Survey;"  south  "1857;"  east,  "Base  No.  9:"  west.  "A.  D.  Bache,  Supt."  The  apex 
is  4  inches  above  its  sides,  and  on  its  foiu'  faces  are  the  letters,  X.  \\.  S.  &  W.  respectively. 


y 


40  THE    EASTERN    OBLIQUE    ARC. 

A  perpendicular  to  the  base  at  the  center  of  the  monument  passes  thron,2:h  the  intersec- 
tions of  cross  hnes  in  copper  boUs  in  tops  of  two  granite  reference  monuments,  3*5  feet 
long  and  i  foot  square,  set  at  distance  of  36  and  72  meters  north  of  station. 

When  the  station  was  visited  in  1884,  these  reference  monuments  were  found 
undisturbed,  also  a  third,  not  described,  with  a  hole  drilled  in  top,  loS  meters  north  of 
the  station.  The  marble  monument  was  then  found  overturned  and  Ijroken,  but  the 
granite  surface  mark  remained  undisturbed,  except  that  the  head  of  the  copper  bolt  had 
been  hammered  so  that  the  cross  lines  were  no  longer  \-isible. 

Epping  ]\\^sf  Base. — This  station  is  about  2  miles  west  of  Schoodiac  Hill,  and  has 
no  subsurface  mark. 

The  surface  mark  is  the  intersection  of  cross  lines  on  a  copper  bolt  in  a  monument 
3  feet  square,  made  from  the  solid  ledge  b\-  cutting  away  the  rock  to  a  depth  of  6  or  8 
inches  around  it. 

vSimilar  marks  i  foot  square  were  made  north  and  south  of  the  center  in  a  line  per- 
pendicular to  the  base,  with  copper  bolts  and  cross  lines  placed  in  jiosition. 

Over  the  surface  mark  was  placed  the  monument  of  marble  of  same  dimensions  as 
that  de.scribed  for  Epping  Ea.st  Base. 

When  visited  in  18.S4  the  niarl)le  monument  was  found  o\'erthrown  and  broken, 
while  the  copper  bolt  had  been  hammered  so  that  no  cross  lines  were  visible.  The  mark 
.south  of  the  center  was  in  perfect  condition.  The  one  to  the  north  had  been  destroyed 
by  vandals,  but  the  remains  of  the  hole  in  which  the  copper  bolt  had  been  placed  could 
be  distinguished.      The  distance  from  the  station  to  these  marks  is  about  10  meters. 

Burke. — This  station  is  on  the  .southernmost  one  of  a  range  of  rocky  hills  about  3 
miles  west  of  Cherryfield  village  and  about  20  rods  north  of  the  line  between  Mount 
Steuben  and  Cherryfield.  It  is  marked  hy  hole  in  a  granite  ledge  at  the  north  end  of  a 
small  hollow  on  the  summit  of  the  hill,  and  it  is  about  3  feet  below  highe.st  part  of  ledge, 
which  is  too  narrow  for  a  signal. 

Tunk. — This  station  is  on  a  mountain  of  the  same  name,  the  most  commanding 
mountain  (except  Mount  Desert)  east  of  the  Penobscot  River.  It  is  about  i  mile  north 
of  the  .stage  road  from  Ellicott  to  Cherryfield  and  about  3  miles  west  of  the  nearest  hou.se 
in  Cherryfield.  It  is  marked  hy  i\  hole  drilled  in  a  granite  ledge  about  150  feet  south- 
we.st  of  the  highest  part  of  the  .summit  and  abcnit  4  feet  below  it. 

Pigeon. — This  station  is  on  the  highest  part  of  a  hill  close  to  the  ocean  on  the 
western  side  of  the  outlet  of  Narraguagus  River.  It  commands  the  coast  from  French- 
mans  Bay  to  Head  Harljor  Island,  and  is  9  miles  from  Cherryfield.  It  is  marked  by  a 
hole  drilled  in  a  flat  rock.  In  range  to  Mount  De.sert,  53'25  feet  distant;  to  Saunders, 
56'25  feet  distant;  to  Humpback,  35 '33  feet  distant,  and  to  Mitten  Mountain,  36'83 
feet  distant,  there  are  holes  and  piles  of  stone. 

Humpback. — This  .station  is  on  the  mountain  of  the  same  name,  near  the  western 
line  of  Brewster  Township.  The  highest  point  of  the  mountain  is  about  400  feet  north- 
east of  the  .station  and  is  4  or  5  feet  above  it.  It  is  marked  by  a  hole  drilled  in  the  rock. 
Range  marks,  con.sisting  of  holes  drilled  in  the  rock  and  heaps  of  .stones,  were  made 
toward  Harris,  .Saunders,  and  Mount  Desert,  distant  14,  17 '42,  and  13 '50  feet,  respectively. 

Mount  Desert. — This  station  is  marked  b\,'  a  copper  bolt  in  a  ledge  which  is  in  the 
center  of  a  small  depression  in  the  large  bare  rock  and  22^  inches  easterly  from  the 
southeast  corner  of  a  crevice. 


BASK    LINKS    AND    HASH    NF;TS.  4 1 

vSingle  range  marks,  consisting  of  a  hole  in  tlie  rock,  were  made  toward  Peaked,  Blue, 
and  Ragged  mountains,  distant  from  center  53 '17,  i7'52,  and  21 '83  feet,  respectively. 
Toward  vSaunders  and  Harris  there  were  two  such  marks,  distant,  in  the  first  instance, 
35*92  and  i42'5o  feet,  while  in  the  latter,  i9'92  and  i36"r)0  feet  from  tlie  center  of  the 
station . 

Howard. — This  station  is  on  a  steep,  precipitous  hill,  about  6  miles  below  Machias- 
port  and  near  Bucks  Harbor.  It  is  marked  bj-  a  drill  hole  in  a  rock.  Range  marks 
were  established  toward  Mount  Desert,  Humpback,  and  Cooper,  distant  33 '67,  66 '25, 
and  2 1 '30  feet,  respectively.     When  visited  in  1884,  the  .station  was  recovered. 

Cooper. — This  .station  is  on  the  northern  end  of  the  summit  of  Western  Ridge,  about 
one-fourth  mile  west  of  the  road  running  through  the  village  of  Cooper  and  about 
three-eighths  of  a  mile  northwest  of  Cooper  Church.  It  is  marked  by  a  drill  liole  in  a 
broad,  flat  granite  ledge.  Range  marks,  consi.sting  of  drill  holes  in  the  rock,  were  made 
toward  Mount  Desert  and  Humpback,  di.stant  22 "80  and  I9"65  feet,  respectively. 

2.    THK    MASSACHUSETTS    KASK    MNK,   M.\.SSACHUSETTS,    1844. 
Location,  mcasurcmoit ,  and  rcsii/tino  lojirdi  of  the  Massac/nisctts  />asr  t/>//\  .1/assar///(srtts. 

/,sv/. 

This  base  was  the  third  and  last  one  measured  with  the  Hassler  ba.se  apparatus  and 
followed  within  a  few  months  the  measure  of  the  Kent  Island  ba.se.  Its  site  is  on  the 
Boston  and  Providence  Railroad,  in  Bristol  County,  Massachusetts,  and  about  12  kilo- 
meters (7)^  statute  miles)  to  the  northward  and  eastward  of  Providence,  Rliode  Island. 
An  account  of  this  base  is  given  in  the  Coast  Survey  Report  for  1865,  Appendix  Xo.  21, 
page  189,  and  little  need  be  .said  here  respecting  the  apparatus,  a  description  of  which 
can  be  found  in  the  account  of  the  measurement  of  the  Fire  Island  and  Kent  Island  bases. 
Its  middle  point  is  in  latitude  4i°'58'"9  and  in  longitude  71°  is''3<  the  mean  azimuth  is 
27°  49'"2,  and  its  length  17?^  kilometers  (or  nearly  10^  .statute  miles ).  There  are  Intt 
two  bases  in  the  United  States  (both  in  California)  which  exceed  this  length. 

The  line  was  measured  by  A.ssistant  Edmund  Blunt  during  September,  October,  and 
November,  1844.  As  in  the  case  of  the  two  bases  previously  measured  by  the  Sur\-e\-, 
but  one  measure  was  made.  The  length  adopted  for  the  compound  S-meter  bar  rests 
upon  the  comparisons  of  1844-45,  with  the  resulting  length  of  7'999  8716  meters  at  o  C. 

±        55 
(see  account  of  the  Kent   I.sland  lia.se).      Tlie  mean  temperature  of  the  bar  during  the 
mea.surement  was   14° '92  C.  (or  58° '85   F.  );    the  average  elevation   of    the  apparatus 
above  the  half-tide  level  at  Boston  Harbor  was  44'" "83.     The  record  at  this  ba.se  is  defi- 
cient in  details. 

The  resulting  length  of  the  base  is  as  follows: 

2  165  bo.xes  17  3i9'"'722i 

Correction  for  exccs.s  of  teiiipiTaturi'  -j-  3'23S3 

Correction  for  inclination  —  o's^^g 

Fractional  part  of  a  box  at  Northea.'^t  Base  +  3  9999 
Correction  for  10°  difference  of  teinperatnre  for  above         —    o"ocxj3 

Additional  lenf>th  measured  by  scale  -r  OM012 

Reduction  to  lialf-tide  level  —  o"i22o 


Resulting  lenglli  of  base  17  326"''376^ 


4: 


THE    EASTERN    (~)BLIOUE    ARC. 


To  form  an  estimate  of  the  accuracy  of  this  measure,  we  find,  from  the  probable  error 
assigned  to  the  base  bars,  that  of  the  base  to  be  d=  o"''oi  19.  With  reference  to  tempera- 
ture, 702  boxes  were  laid  with  rising  and  579  with  falling  temperature,  and  for  the  rest 
of  the  boxes  the  temperature  was  stationary.  The  assumed  probable  error  from  this  con- 
dition and  probable  lag,  and  from  gradtiation  error  is  zbo'"'0332,  and  the  probable  error 
from  instability  of  the  microscopes  is  taken  as  =bo"''oo59.  Combining  these  three 
independent  values,  we  get  for  tlie  probable  error  of  the  base  d=  o'" '0358,  which  equals 
We    have,    therefore,   the    final    result  for    the    length    of    the 


4  8  3^80    oi  its  length 


Ma,s.sachusetts  base  17   326'3763  meters,  and  its  logarithm  4'23.S  70774. 


± 


•035« 


± 


90. 


No.  5. 


BLwe  JIM 


'Jlic  con)u:ctio)i  of  the  Massacliusctts  base  ~n'ith  tlic  Diaiii  triaiiff illation . 

The  Ma.s.sacliusetts  base  is  connected  with  the  main  triangulation  in  an  unusual 
way — that  is,  with  a  ba.se  net  so  simple  as  to  render  a  .special  adju.stment  of  it  unnece.ssary. 
The  conditional  equations,  therefore,  which  sub.si.st  between  the  three  northern  base 
lines  were  extended  to  reach  directly  to  the  Mas;:achusetts  base  without  any  interven- 
tion of  a  .special  ba.se  net  adjustment. 
The  diagram  shows  the  direct  con- 
nection of  the  ba.se  with  the  triangtila- 
tion  of  the  New  England  States,  the 
quadrilateral  Beacon  Pole,  Copectit, 
Manomet,  and  Blue  Hill  being  an 
integral  part  thereof.  One  advantage 
which  the  base  po.s,ses.ses  over  the 
other  two  is  its  great  length. 

The  following  table  gives  the  ap- 
])roximate  elevation  above  the  Atlantic 
(if  tile  stati(jns  adjacent  to  the  base: 

Meters.  Feet. 

Ma.s.sachusetts  vSoutli  Base 33  108 

MassachiLsetts  North  Base 70  23 1 

Beacon  Pole 167  548 

Great  Meadow  .So's  264 

Copecut 107-5  353 

Maiioniet 1 20  394 

Blue  Hill   194  635 


rCopccut 
Statut*  Miles 


10 


O  10 

Kilometers 


20 


10 


10 


20 


30 


40 


Di'scriptioits  of  stotioiis. 

The  descriptions  of  these  old  stations  are  very  meager.  The  following  information  is 
all  that  could  be  gathered: 

J/assac/iKSt'tts  Soitt/i  Base,  /(Vy/. — The  station  is  located  on  the  Boston  and  Pro\-idence 
Railroad,  in  Bristol  Countw  Ma.ssachu.setts.  For  a  ground  mark  a  stone  of  the  follow- 
ing dimensions  was  buried:  Length,  4  feet  7  >4  inches;  base,  12  inches  square;  top,  6  inches 
square.  A  copper  bolt,  on  which  there  is  a  cro.ss  mark  (  +  ),  driven  in  t^^e  stone  defines 
tile  starting  point  of  the  measure.  The  stone  is  S  feet  from  the  ea.stern  rail  of  the  Boston 
and  Trox-idence  Railroad,  there   Ijeing   but   one   track   laid.      "  .Another  stone  is  placed 


I 


BASH    LINES    AND    BASE    NETS.  43 

oil  the  west  side  of  the  road  in  the  hue  toward  ]5eaconpole  Hill,  6  inches  heinj^  above 
gnnind,  and  distant  33  feet  from  the  termination  of  the  base."  * 

Massachusetts  North  Base,  18^^. — The  station  is  marked  hy  a  Ijrick  tower,  stated  by 
G.  Bradford  to  be  44  feet  in  height,  when  reoccupied  October  18,  1884.  The  center  of 
the  station  is  indicated  by  a  brass  Ixjlt  in  the  center  of  a  stone,  thus  + .  It  is  central 
with  the  tower.     The  cap  .stone  (of  1844)  had  a  mean  diameter  of  o'32  meter. 

Bcaconpole,  184^.  — This  statical  is  located  al)out  2  miles  northeasterly  from  the  village 
of  Cumberland  Hill.  The  station  was  visited  and  reoccupied  in  vSeptemlx;r,  1884,  by 
Assistant  G.  Bradford,  who  remarks:  "Found  here,  guided  by  K.  H.  Pickering,  an 
old  resident,  a  copper  (brass?)  bolt  set  in  lead  and  filling  a  hole  drilled  in  a  ledge  of 
rock  .some  30  feet  in  diameter,  which  occupies  the  summit  of  the  elevation."  A  tripod 
signal  was  built  over  the  station  in  1884.  There  is  also  a  description  of  1896  by  H.  B. 
Wood,  of  the  "  vSurvey  of  the  Commonwealth  of  Mas.sachusetts. " 

Copecut,  1S44. — Station  on  Copecut  Hill  between  Fall  River  and  New  Bedford.  As.sist- 
ant  G.  Bradford  found  here  in  November,  1884,  a  copper  bolt  in  a  rock,  presumably 
the  center  of  the  station.  A  large  pile  of  stones  was  found  about  the  bolt,  covering  it. 
The  place  is  surrounded  with  bushes  and  small  trees,  and  is  difficult  to  find  without  a 
guide.  The  road  to  it  through  the  woods  is  extremely  rough.  A  tripod  signal  was 
built  here  in  1884. 

Great  Mcadozc,  184J. — This  is  one  of  the  Borden  Survey  stations;  about  3  miles  north 
of  west  of  Rehoboth  village,  7  miles  from  Taunton,  and  12  from  Providence,  Rhode 
Island.  A.ssi.stant  G.  Bradford,  in  September,  1884,  found  here  a  hole  in  the  rock, 
where,  an  old  resident  says,  the  signal  once  stood.  The  trees  have  grown  up,  and  are 
now  to  the  northward  and  westward  some  40  to  50  feet  high.  The  following  descrip- 
tion is  by  Assistant  C.  H.  Van  Orden,  in  i88g:  'The  hill  is  well  known  and  is  called 
Great  Meadow  Hill  by  the  people  about  North  Rehoboth.  It  is  best  approached  from  the 
south  side.  It  is  a  large  flat  hill,  with  a  growth  of  timber  on  the  east  and  west  sides. 
Directly  north  of  the  station  is  an  open  lot  or  meadow,  noticeable  from  a  di.stance." 

Manomct,  18-I.5. — Near  Plymouth,  Ma.ssachu.setts.  A.ssistant  C.  O.  Boutelle  states,  in 
his  record  of  the  latitude  observations  of  July,  1867:  "  The  triangulation  .station  at 
Manomet  has  been  more  permanently  marked  l)y  drilling  three  holes,  forming  an  equi- 
lateral triangle  around  the  copper  bolt,  and  each  hole  is  distant  6  inches  from  it.  The 
two  holes  south  of  the  bolt  are  east  and  west  from  each  other  antl  the  third  hole  is  north 
from  the  bolt.  Each  hole  is  five-eighths  of  an  inch  in  diameter  and  2  inches  deep."  In 
September,  1877,  Assistant  G.  A.  Fairfield  writes:  "Visited  this  .station  and  found  it 
undisturbed;   had  no  difficulty  in  finding  the  rock  with  copper  bolt  and  three  drill  holes. 

Blue  Hill,  i^-l-S- — Near  Dedham,  Massachusetts.  The  Coast  Survey  station  is 
distant  from  the  Borden  survey  .station  of  Blue  Hill  8^337  meters,  and  the  azimuth  of 
the  Borden  .station  is  11°  16',  as  deduced  from  computation  of  December,  18S4.  The 
Borden  station  was  located  in  the  middle  of  a  .square  inclosure  of  stones.  In  November. 
1886,  A.ssistant  C.  H.  ^'an  Orden  visited  the  station  and  found  the  Coast  Survey  copper 
bolt  (outside  the  old  Borden  inclosure)  in  gooil  order.  Borden's  "  Blue  Hill"  is  under 
the  stone  tower  of  the  "  Blue  Hill  Observatory.  " 

The  private  meteorological  ob.servatory  at  this  place  was  e.stablished  by  Mr.  A.  L. 
Rotch  in  1885.  It  is  a  two-story  circular  tower,  12  feet  in  diameter  in.side  and  25  feel 
high,  l)uilt    of   the    l)roken   stone   fmind  on  llie   liill.       I'!xtending   southward   from   this 

*  l-roin  original   rcionl  ol    the  hasc  iiicasurt  nutil. 


44  I'HE    EASTERN    OBLIQUE    ARC. 

tower  is  a  one-story,  hip-roof  liouse,  built  of  stone,  with  a  wooden  shed  attached.  (See 
heUotype  in  Annals  of  the  Astronomical  Observatorj'  of  Harvard  College,  Volume  XX, 
Cambridge,  1896).  There  is  also  a  description  of  1896  by  H.  B.  Wood  of  the  "Survey 
of  the  Commonwealth  of  Massachusetts. ' '  A  sketch  shows  the  Coast  vSurx'ey  station 
with  reference  to  the  tower. 

3.    THK    FIKK    ISLAND    BASE    LINE    AND    BASE    NET,   NEW    YORK,    1834. 
/vocation,  vicasuriinoii,  a?id  >rsii/thig  /oigt/i  of  the  Fire  Island  Base  Line,  New  York,  i8jif. 

The  site  of  this  base  is  on  the  southern  shore  of  Long  Island,  New  York,  on  the 
narrow  Fire  Island  beach  between  the  Great  South  Bay  and  the  Atlantic  Ocean,  and 
distant  nearly  So  kilometers,  or  50  statute  miles,  to  the  east  from  New  York  City.  It 
was  the  first  and  only  primary  base  measured  bj' Superintendent  F.  R.  Has.sler,  and  the 
measurement  was  made  with  an  apparatus  of  his  own  design.  He  has  left  a  full  descrip- 
tion, with  illustrations,  in  detail,  of  this  apparatus  in  the  Transactions  of  the  American 
Philosophical  Society,  Philadelphia,  Pennsylvania,  new  series,  1825,  Volume  II,  pages 
273-2S6.  The  essential  parts  of  the  apparatus  are  enumerated  in  No.  12  of  his  cata- 
logue of  instruments,  which  probably  dates  back  to  the  year  18 16.  These  parts  appear 
to  have  been  made  by  Troughton,  of  London,  in  18 13.  Two  other  primary  base  lines 
were  measured  with  the  same  apparatus,  viz,  the  Kent  Island  and  the  Massachusetts  bases. 

The  beach  over  which  the  measure  extended  is  sandy,  interspersed  with  low  hum- 
mocks and  ridges,  and  subject  to  changes  from  storms,  which  caused  the  west  end  of  the 
base  to  be  finalh*  lost,  notwithstanding  a  strong  timber  protection  surrounded  the  hillock. 
The  eastern  terminal  point  was  further  removed  from  the  beach,  which  caused  a  bend 
in  the  line  close  to  the  monument,  and  necessitated  the  measure  of  an  angle  at  the  bend. 
The  insecurity  of  this  exposed  base  and  the  danger  of  its  loss  caused  the  transfer  of 
its  length,  a  few  years  later,  to  be  made  to  a  primary  line  located  on  the  central  hills 
of  Long  Lsland.      The  base  net,  therefore,  in  this  case  consists  simph'  of  a  quadrilateral. 

The  length  of  the  base  is  about  14  kilometers  (or  8%  statute  miles).  The  central 
point  is  in  latitude  40°  38' '9,  and  in  longitude  73°  o8''i.  The  mean  of  the  forward  and 
backward  azimv;ths  is  72°  56' '8.  For  convenience  of  reference,  a  brief  description  of 
the  Hassler  base  apparatus  is  repeated  here  from  his  description,  and  further  remarks 
on  this  subject  will  be  found  in  connection  with  the  Kent  Island  base.  It  makes  use 
of  one  measuring  bar  and  of  optical  contact.  The  bar  is  8  meters  in  length  and  is 
composed  of  four  2-meter  iron  bars  placed  in  contact  lengthwise.  These  pieces  are  of 
square  section  *  and  are  firmly  held  together  l).v  means  of  collars  clamped  over  the  bar 
ends  and  bringing  them  together  by  means  of  .screw  bolts.  The  whole  or  compound  bar 
is  supported  on  15  rollers,  resting  on  a  wooden  beam,  itself  adjustable  upon  another 
similar  support.  The  whole  is  placed  in  the  bottom  of  a  wooden  trough.  There  are 
eight  thermometers,  two  placed  on  the  upper  surface  of  each  of  the  single  bars  to 
ascertain  their  temperature.  A  sector  for  measuring  the  inclination  is  attached  to  one 
end  of  the  supporting  beam,  and  all  required  mechanical  appliances  for  the  adjustment 
and  alignment  of  the  bar,  as  well  as  for  the  manipulation  of  the  micrometer  micro- 
scopes, are  provided.  The  trough  itself  rests  upon  five  trestles.  The  two  microscopes 
are  likewise  mounted  upon  trestles.  For  alignment  of  the  base  the  trough  or  box 
carries  at  one  end  a  small  telescope  and  at  the  opposite  end  a  short  vertical  pin  to 

*The  same  as  that  of  the  Committee  Meter, 


FERDINAND  RUDOLPH   HASSLER   (1770   1843). 


HASH  ijnp:s  and  hasp:  nets. 


45 


define  the  axis  of  the  apparatus  and  the  direction  of  the  Hne  of  measure.  The  micro- 
scopes admit  of  adjustment  for  verticahty  of  axis.  Their  objectives  are  composed  of 
two  half  lenses  of  different  foci,  one  ior  pointing  on  spider  tlireads  stretched  across 
small  central  half-circular  notches  cut  vertically  into  the  end  faces  of  the  protrudinj( 
measuring  bar,  the  other  focus  serving  for  a  verification  of  the  steadiness  of  the  optical 
axis,  the  pointing  being  made  upon  cross  lines  ruled  on  an  ivory  ])late  resting  ou  the 
support  below  the  microscope. 

For  the  standardization  (jf  the  measuring  bar  repeated  comparisons  were  made  at 
difTerent  times  by  different  ol)servers  and  by  different  means.  The  Hassler  double  end- 
meters,  known  as  bars  A,  B,  C,  and  I),  were  first  compared  in  Februar\' and  March,  isiy, 
with  the  Committee  Meter  and  a  .standardized  iron  a  bout  meter  by  Lenoir.  In  the  same 
year  Hassler  determined  their  coefficient  of  expansion  and  found  it  o'ooo  006  963  for 
Fahrenheit's  scale  or  o'ooo  012  534  for  the  Centigrade  scale,  a  value  somewhat  large  \et 
probably  applying  to  these  particular  bars,  but  this  could  not  l)e  verified,  the  bars  having 
long  since  been  lost.  In  May,  1S34,  and  March,  1835,  in  connection  with  the  Fire  Island 
ba.se,  comparisons  were  made  involving  the  Troughton  brass  scale  and  the  Connnittee 
Meter.  The  last  compari.sons  date  from  1 844-45 ,  and  were  made  with  a  Bessel  level-contact 
comparator,  using  the  Lenoir  iron  meter.     The  results  were,  for  the  combined  lengtli 

ato°C: 

From  coniparison.s  of  1S17      2  =  7"''999  9506 
From  comparisons  of  1S34-35  8"ooo  0414* 

±     242 
FVoni  compari-soiis  of  1S44-45  7 '999  >'^7i6 

r+T         55 

When  the  comparisons  in  1835  in  connection  with  the  Fire  Island  base  had  l)een 
made  an  examination  of  bars  A  and  B  showed  them  to  be  rusty.  After  cleaning  them 
they    were     again    com-  ^.  _  ^ 

pared,  and  the  new  1835 
value  ^=  7"'"999  9764  re- 
sulted. The  last  ob.ser- 
vations  indicate  a  decided 
apparent  shortening, 
which  has  not  been  ac- 
cotinted  for  satisfactorily 
except  it  be  due  to  the 
manner  in  which  the 
8-meter  bar  was  built  up. 
Upon  the  whole,  it  has 
been  thought  best  to  adopt 
the  Has.sler  value  of 
1834-35  for  the  reduc- 
tion of  the  Fire  Island 
base  as  representing  the 
conditions  then  existing. 

But  one  measure  of  the  base  was  made,  owing  probably  to  the  labor  and  time 
required  to  measure  such  a  long  line.  The  measure  was  made  during  the  months  of 
August,   September,  and  October,  1834.     The  above  diagram  shows  the  condition  at 


East  Monument 

U 


*The  v.iltif  fdiiiul  in  odntiectioti  with  the  Kire  Islaiul  txise. 


46  THE    EASTERN    OBLIQUE    ARC. 

the  eastern  end.  The  distances  2  to  3,  3  to  4,  and  4  to  5  were  measured  with  the  base 
apparatus,  and  the  angular  horizontal  directions  of  the  fine  and  heavy  lines  at  the 
points  I,  2,  3,  4,  and  5  were  obtained  by  means  of  a  theodolite.  Calling"  West  Ba.se 
No.  6,  the  points  6,  5,  4,  and  3  were  placed  in  line.  For  reduction  of  the  measured 
length  of  the  base  to  sea  level,  the  average  height  of  the  bar  above  the  half -tide  level 
of  the  Atlantic  was  taken  as  2 '75  meters.  The  mean  temperature  of  the  bar  during 
measurement  was  26° '60  C.  (or  79° '90  F.  ).  The  resulting  length  from  West  Ba.se  to 
East  End  was  as  follows: 

I  725  boxes  13  800"^ '07 14 

Correction  for  excess  of  temperature  over  o°C  +  4'6o3i 

Correction  for  inclination  —  0'2055 

Reduction  to  half-tide  level  of  ocean  —  o'oo6o 


Resulting  length  13  So^""4630 

Similarly  we  have  the  short  measures  at  the  eastern  end. 

Line  measured  2  to  3  5  to  4  3  to  4 

Number  of  boxes  14  17  7 

Corre.sponding  length  ii2"''ooo6  I36"''ooo7  56""ooo3 

Correction  for  expan.sion  -fo'02i6  ^o"0276  -j-o'cirg 

Correction  for  inclination  — o'o65o  — o'o268  — 0*0038 

Defect  of  last  bo.x  at  eastern  end  -f'0'8203  4-i'i38o 


Resulting  length  H2"'7775  i36'"-ooi5  57'"T464 

In  the  adjustmewt  of  the  linear  and  angitlar  mea.stu'es,  it  has  lieen  a.sstuned  that  the 
former  require  no  correction;  the  figure  adjustment  of  i,  2,  3,  4,  and  5  involves  two 
angle,  two  side,  and  two  distance  or  length  equations,*  and  the  resulting  length  for  line 
5  to  1  was  294'752  meters.  If  West  Ba.se  l)e  designated  as  6,  then  by  the  known  dis- 
tances 6  to  5  and  i  to  5  and  the  known  angles,  the  angle  at  6  between  East  F^nd  and 
East  Base  is  found  equal  to  36'  41" '3,  whence  the  final  length  We,st  Ba,se  to  East  Base 
l)ecomes  14  05.S'g709  meters  and  its  logarithm  4' 147  953  53. 

To  ascertain  the  probable  error  of  this  result,  we  estimate  that  of  the  line  6  to  5  as 
d=o""oooo242  for  each  box,  hence  for  thewhole  di.stance  ±o""o4i7.  Respecting  the  tem- 
perature of  the  bar,  455  boxes  being  placed  with  rising  temperatttre,  553  with  .stationary 
temperature,  and  717  with  falling  temperature,  and  a.s.suming  a  po,s.sible  error  in  temper- 
ature of  2°,  the  probable  error  of  the  base  might  be  it  o"''029.  The  effect  of  the  gradu- 
ation error  is  estimated  at  d=o"''023  or  ±o"'"037o  for  combined  effect.  The  probable 
error  arising  from  instability  of  microscopes  was  assumed  to  be±o""ooo  127  and  the 
total  effect  d=  o'"'oo53.  These  are  the  principal  .sources  of  error  and  when  combined 
produce  ±:o"''057  for  the  line  6  to  5.  To  obtain  the  probable  error  for  the  line  between 
the  monuments  =ho"''oi3  was  added,  hence  the  probable  error  of  the  base  as  e.stimated  is 
v/(o-o57)'+  (o-oi3)^  =  ±o""o585. 

This  equals —  part  of  the  whole  length,  the  corresponding  \-altie  \n  the  loga- 

rithm  of  the  length  =t      -, —  =  o '000  001  807.       Consequently,   the  final  result  for  the 

1       .1      f.i     T7-      Ti      lu        •     14058-9709  4'i47  953  53 

length  or  the  Frre  Island  ba.se  rs  ,  ,,     meters,  arrd  rts  logarrthm    ,  ,, 

''  zt    0585  '  ±  I  8r 


♦All  measures  involved  in  this  adjustment  were  found  satisfactory. 


HASIv    LINKS    AND    liASK    NKTS.  47 

Thr  l-iit   hidiid  base  net  and  ycsitlls  of  its  adjuslnicnl. 

In  this  net  we  iiu-liuk-  llie  (iiiadrilateral  whicli  transfers  tlie  measured  hase  to  the 
so-called  mountain  base,  and  the  two  other  quadrilaterals,  one  within  the  other,  which 
start  from  this  derived  l)ase.  The  line  Wooster  to  Sandford  will  he  the  connecting  link 
with  the  northeastern  trian^ulation,  and  the  line  West  ^^  - 

Hills  to  Bald    Hill  will  form   the    link    for    tlie   soutli 
western  l)ranch. 

The  elevations  of  the  stations  ahoNx-  the  sea  le\-el 
are  verj-  moderate  and  the  horizontal  directions  needed 
but  very  small  corrections,  the  maxinunn  bein^^  less 
than  o"'o2,  but  no  account  of  this  was  taken  when 
less  than  o"oo3.  The  approximate  hei<jhts  of  the 
trigonometric  stations  are  as  follows; 


Meters. 

Ktet. 

West  Hills  [17 

3S3 

Riilaiid         104 

341 

Tashua  ■•      i<S5'3 

608 

Bald  Hill     196 

643 

Woostet       305 

I  000 

Sandford     27-^ 

S95 

Fire  Islojui  West  Base 

Kiloniot  er  .'^ 


The  ends  of  the  liase  are  between  2  and  3  meters 
above  the  sea.  In  this  figure  we  ha\-e  a  coml)ination 
of  verj' old  work  with  later  work.  The  measures  of 
horizontal  angles  by  Stiperintendent  Hassler  date  from 
1833  and  were  made  with  a  60""  theodolite,  first  em- 
ployed at  station  Weasel  in  1817.  Subsequently  he 
used  the  75""  theodolite,  first  employed  at  station  West 
Hills  in  1836.  This  last  instrument  was  in  continu- 
ous'tise  till  November,  1S73,  when  it  met  with  an  acci- 
dent at  station  Sawaiee,  Georgia.  It  was  struck  In' 
a  tornado  and,  notwithstanding  its  weight  of  300 
pounds,  was  hurled  from  its  .stand  and  irrejxnabh- 
damaged. 

In  consequence  of  the  work  added  between  1862  and  1865,  and  the  reoccupation  of 
three  of  the  old  stations,  a  new  adjustment  of  the  base  net  became  uecessar\ .  Weights  had 
to  be  introduced  in  consequence  of  the  unequal  values  of  the  resulting  t'irections  due  to 
the  relatively  small  number  of  series  in  the  older  work.  It  was  dttue  by  the  same  method 
as  already  explained  in    connction  with  the  adjustment  of  the  Epping  base  net.      From 

the  closing  of  17  triangles  we  haw  the  mean  error  of  a  triangle  ./    ~     ^"'  ^  ±  o""S4  antl  of 


Sandford 


10 


O  10  20 

Statute  Miles 


an  angle 


0-84 


049, 


.      =^  zfc  o"'4g  and  theprol)able  error  of  a  direction  o'074  \  —y^ 
V  3  ■v^- 


The  approximate  average  probable  error  of  a  (.lnecti(.)n  from  station  adjustment  result- 
ing from  36  directions  is  e^=  zto"H).  hence  the  square  of  the  triangle  combination 


*l)fnveil  from  siiirit  levels. 


48 


THE    EAvSTERN    OBLIQUE    ARC. 


error  r  equals  (o"23)^— ( o'lg )"  or  f,  =  ±  o"'i3,  that  is,  the  combination  error  is  but 
shghtlv  less  than  the  observing  error  e^^.  If  t'\  is  added  to  each  value  of  <'\  we  get 
the  weight  of  each  direction  />  =  i/{e\-\-e'J.  Among  the  values  of  e^  there  was  one 
exceptionally  large,  and,  omitting  it,  we  find  t'^  =  ±  o""i8,  hence  e^  =V(o'233)° — (o'lSs)" 
=  =b  o' i44and/i  =  1/ [(  o"i44)'+ (',,']  .  and  in  order  to  make  the  average  sum  of  the  recip- 
rocals of  the  weights  nearly  unity,  the  values  of  i/p  were  multiplied  by  13.  The  range 
in  these  relative  weights  is  still  -large,  the  ratio  of  the  greatest  to  the  least  being  as  16 
to  I,  but  it  would  have  been  as  144  to  i  had  not  the  equalizing  device  been  introduced. 
Comparing  the  old  with  the  present  results  they  are  found  to  be  nearly  the  same.  For 
the  side  Wooster  to  vSandford  we  have  old  log.  distance  ( Coast  Survey  Report  for 
1865,  pages  201-202)  4"669  171  i  and  by  the  present  adju.stment  4-669  171  o,  which 
log.  difference  corresponds  to  a  linear  difference  of  but  2  centimeters.  For  the  side  Bald 
Hill  to  West  Hills  we  have  old  log.  di.stance  ( Coa.st  Survey  Report  for  1866,  page  52) 
4-648  135  3,  and  by  the  present  adjustment  4-648  135  6,  corresponding  to  a  linear 
difference  of  4  centimeters. 

A  preliminary  publication  of  results  of  the  triangulation  about  this  ba.se  and  vicinity 
was  made  in  185 1  in  the  Coast  Survey  Report  of  that  date,  pages  222  and  following.  A 
second  publication  will  be  found  in  the  Coast  Survey  Report  for  1865,  pages  201-202. 
These  results  are  now  superseded. 

Abstracts  of  horizontal  directions  at  stations  formimr  the  Fire  Island  lUxse  Net.     /Sjj-/S6_). 

Fire  Island  East  Base,  Suffolk  County,  New  York.     October  i   to  October  8,  1S37.     F.   R.   Has,sler, 
observer.     75*-"'  ilirection  theodolite  No.  i.     Circle  used  in  V!  positions. 


No.  of 
ilirectioiis- 


<Jhject  observed. 


Fire  Island  West  Base 
West  Hills 
Ruland* 


Re.sulting  direc- 

tion.s  from  .station 

adjvistnient. 

Approximate 

probable 

error. 

Correction 

from  net 

adjustment. 

0         / 

// 

/' 

// 

0     00 

00  'GOO 

±0-32 

+  0  -426 

44     48 

25  -129 

0  -27 

-   1  -086 

112     32 

52  -^03 
f  0  -022 

0  '22 

+  0  -330 

Final 

seconds. 


GO  "426 
24  -043 
52-755 


Fire  Island  West  Base,  Suffolk  County,  New  York.     October  16  to  October  24,  1837.     F.  R.  Hassler, 
ob.server.     75""  direction  theodolite  No.  i.     Circle  used  in  VI  positions. 


West  Hills 
Ruland* 

Fire  Island  Ea.st  Base 


0 

OG       00  '000 

±0-30 

+  0  -397 

00-397 

73 

39    46-131 

+  0  -087 

0  -19 

-  0  -386 

45  -832 

113 

49     51  -571 

G  -29 

+  O-I5S 

51  -729 

*The  correction  for  eccentricity,  as  indicated,  refers  to  Ruland  of  1865  since  the  station  occupied  in  1865  does  not 
jjerfectly  agree  with  the  old  station  of  1837. 


BASE   LINKS   AND    BASH   NETS. 


49 


Abstracts  of  horizontal  directions  at  stations  fonnini;  the  hire  Island  base  net,  /^jj-/<?65:— continued. 

Ritland,  Suffolk  County,  New  York.  Auj^ust  19  to  September  16,  1837.  F.  R.  Hassler,  observer. 
75""  direction  theodolite  No.  i.  Circle  used  in  VI  ])ositions.  June  11  to  July  27,  1865.  G.  W. 
Dean,  ol)server.     Same  instrument.     Circle  u.sed  in  V  positions. 


(  Fire  Island  Ea.st  Base 
I'ire  Island  West  Base 

We.st  Hills 


West  Hills 
Wooster 

Tashua* 

Sandford* 

Adopted  results  at  Ruland: 


No.  of 
direction.s. 


Object  observed. 


o      00      00'00<J 

27     17     o2'65i 

+0-065 

78     54     o2-22r 

•  o-i  14 

o     00     OO'OOO 

26  28-009 
40-047 

59  43  262 
'  0-047 

19  14-917 
+0-047 


±0-14 


61 


73 


=bo-o9 
0-08 

0-07 

009 


Resultiiie  di- 
rections from 
station  ad- 
justment. 


Ap- 
proxi- 
mate 
prob- 
able 
error. 

// 


Reduc- 
tion to 

sea 
level. 


Seconds 

reduced 

to  sea 

level. 


Correc- 
tion 
from 

net  ad- 
just- 
ment. 

// 


9 
10 
II 
12 

13 


Fire  Island  East  Base 

Fire  Island  West  Base 

We.st  Hills 

Bgld  Hill  t 

Wooster 

Tashua 

Sandford 


— O  "020 
-0-310 


56-721 
30-373 

45  636 
17 '303 


-ro  '266 
+0-131 
-ro  -040 
— o.  134 
—  0192 


Final 
sec- 
onds. 


o  00     00-000        ±0-74  

27  17      02  -716         ■      O  '22  

7S  54    02  -335  0-35  

132  oS     56-733  0-27        -0-012 

140  20    30-391  0-08       —0-018 

152  53     45  '644  o  -07       — o  -ooS 

iSo  13     17-299  0-09        f  o -004 

JF<?5/ /////.?,  Suffolk  County,  New  York.  October  18  to  December  1,  1S36.  F".  R.  Hassler,  observer 
ygim  direction  theodolite  No.  i.  Circle  used  in  VI  positions.  July  18  to  August  15,  1S65.  G.  W 
Dean,  observer.     Same  instrument.     Circle  used  in  V  positions. 


59-980 
02  -406 
02  -601 
56  -852 
30-413 
45  502 
'7  "495 


RulanJ. 

0 

00 

00  -000 

±0-31 

F^ire  Lslaiid 

East  Base 

33 

21 

31  -070 
-0-136 

o"33 

Fire  Island  West  Base 

54 

43 

16  -203 

0-38 

-0-136 

Wooster 

0 

00 

00  -000 

+:0-o6 

Azimuth  Mark 

7 

26 

21  -398 

0  -06 

•  0  -370 

Tashua 

21 

35 

06  -485 
0  -009 

0-05 

Sandford 

33 

5S 

36  '554 
0  -023 

o-oS 

Ruland 

89 

14 

44-819 

0  -07 

— 0  -078 

*  The  correction  -fo"-o47  refers  to  the  direction  of  heliotrope  to  station  of  iSj6;  the  other  corrections  refer  the  old 
measures  to  Ruland  station  of  1865.  since  the  stations  of  iS;;  and  1S63  do  not  quite  coincide.  No  notice  is  taken  of  those 
observations  of  1S37  which  are  superseded  by  new  observations  of  1S65, 

tMean  value,  as  derived  difTerentially  from  We.st  Hills  and  Tashua. 


4192 — No.  7 — 02- 


-4 


50  THR    EASTERN    OBLIQUE    ARC. 

Abstracts  of  horizontal  directions  at  stations  forunni^  tlie  Fire  Island  base  net,  /Sjj-/S6j — continued. 

No  notice  is  taken  of  those  measures  of  1836,  which  are  superseded  by  new  measures  of  1865.  The 
corrections  for  eccentricity  are  indicated;  instead  of  increasing;  the  direction  to  Ruland  by  o"'i36  this 
anioutn  is  subtracted  from  the  measures  of  the  base  ends. 

Kesnitinx  directions  at  West  Hills: 


No.  of 
directions. 


Object  observed. 


Resulting  di- 
rections  from 
station  ad- 
justment. 


Ap- 
proxi- 
mate 
prob- 
able 


Reduc- 
tion to 

sea 
level. 


Seconds 

reduced 

to  sea 

level. 


Correc- 
tion 
from 
net  ad- 
just- 
ment. 


Final 
sec- 
onds. 


15  Wooster                                  o  00     00  000       zbo '06       —  o '003       59 '997  -!-o'i69       00 '166 
AzimuUi  Mark                       7     26     21  768           o  -06           

16  Tashua                                  21  35     06 '476           o '05       +0 '006       06 '482  —0-099       06-383 

17  vSandford                               33  58     36-531           0-08       +0-014       36 '545  —0-089       36-456 

18  Rnlantl                                  89     14     44-741           0-32           +0-226       44-967 

19  Fire  Island  East  Base      122     36     15-675           0-33           —0-400       15-275 

20  Fire  I.sland  West  Base      143     58     00  -80S           0-38           +0  -406       01  -214 

Harrow*  269     17     04-256  0-16  

Round  Hill*  331     59     49-211  0-33  

14            Bald  Hill*     .                     359  21     01-916           0-25       —0-003       01-913  —0-123       01-790 

Tas/nia,  Fairfield  County,  Connecticut,  August  25  to  September  16,  1833.  F.  R.  Hassler,  observer. 
75"'"  direction  theodolite  No.  i.  Circle  used  in  III  positions.  September  2  to  October  21,  1863. 
G.  W.  Dean,  observer.     Same  instrument.     Circle  u.sed  in  V  positions. 


30 

Ruland 

31 

West  Hills  t 

32 

Bald  Hill  J 

33 

Wooster 

Good  Hill 

29 

Sandford 

Mount  Carmel 

0 

00 

00  'OOO 

d=0-0S 

-|-  0  -082 

00-082 

38 

20 

42-522 
+0  -023 

0  -09 

+0  -0S5 

42  -630 

96 

34 

59  +38 

0-44 

+  0-006 

59  '444 

+0  -07S 

59 '522 

138 

32 

49  -096 

0  -06 

-0-015 

49  -081 

— 0-241 

48  -S40 

200 

12 

56  -834 

0  -08 

249 
259 

56 
24 

26  -327 
22  -837 

0  -06 
0  -12 

40-017 

26  -344 

+0  -107 

26-451 

Sandford,   New   Haven    County,  Connecticut.      September   9    to    November  4,   1862.     G.   W.   Dean, 
observer.     75'"'  direction,  theodolite  No.    1.     Circle  used  in  V  positions. 


21 

Ruland 

0 

00 

00  -000 

22 

We,st  Hills  t 

23 

24 

41  "547 

+  0  -QOS 

23 

Tashua 

42 

36 

58-413 

24 

Wooster 

69 

03 

33-113 

Azinuith  Mark 

85 

20 

30  -246 

Ivy 

147 

34 

47  -646 

Mount  Tom 

190 

09 

54-581 

Box 

221 

37 

22  062 

Mount  Carmel 

298 

46 

oS  -532 

d=0  -I  I 
0-12 

0-12 

o  -24 
0-I5 
0-15 

O  -12 

o  -10 

0-44 


-0  -01  I 
-0  -009 


58  -424 
33-122 


-o  -264      59  -736 
-o  -482      42  -037 


-o  -330 

+0  -356 


*'rhe  results  are  mean  values  derived  differentially  from  Tashua  and  Ruland. 

1  Correction  for  eccentricity  indicated. 

J  Mean  value  deduced  from  differences  with  West  Hills  and  Ruland  in  1833  and  1863. 


58  -094 
32  -478 


BASE    LINKS    AND    HASK    NF;TS. 


51 


Absha^ls  of  hori':o)ilal  directions  at  stations  foniiiiii^  llic  /•'ire  /stand  luisc  net,  /8jj-/86^ — continued. 

Woostcr,    P'airfield    Count)-,    Connecticut.      July    14    to    October    10,    1864.      V,.   W.   Dean,  observer. 
75""  direction  theodolite  No.   i.      Circle  used   in  \'  jjositions. 


No.  of 
direction.s. 


25 
26 

27 
28 


Object  ob.served. 


Ivy 

Sand ford 
Tashua 
Ruland 
West  Hills* 


Resulting  di- 
rections from 
station  ad- 
justment. 

Ap- 
proxi- 
mate 
prol)- 

able 
error. 

Reduc- 
tion to 

sea 
level 

Seconds 
reduced 

to  sea 

level 

Correc- 
tion 
from 

net  ad- 
just 
ment. 

Final 
sec- 
onds. 

0        / 

// 

// 

// 

// 

'  // 

// 

0      (X) 

00  '000 

±0  -07 

53     47 

59  '208 

0-07 

i-o  -009 

59  217 

—0  069 

59->4'S 

95     57 

47  -652 

o'oS 

—0  -009 

47  '643 

-f-O  -285 

47  •928 

124     51 

45  '93^ 

0  -08 

^0  -005 

45  -943 

154     10 

3S  -493 

0  -07 

-0-I47 

38  -378 

Bald  Hill,   Fairfield    Cotinty,   Connectictit. 


+  o  "032 
July   23   to  August    18,  1833.      I'.    R.    Hassler,   observer. 


60'"'  direction  theodolite  No.  2.     Circle  used  in  VI  positions. 


34 

Tashua 

35 

Ruland 

36 

West  Hills 

Harrow 

Round  Hill 

I 

II 
III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 

XIV 

XV 

XVI 


o  00 

62  40 

99  31 

121  42 

15S  36 


00  000 
12  '802 
-  o-o56t 
40  -835 
1 8  '609 
54  "002 


=hO  '22 
O  '60 

0-27 
0-19 

o  '40 


o  •006    00  006 


-0103    59-903 

-^1-433     14-291 
—0-213     40-622 


FIRK    ISLAND    li.ASF,    NF/f. 

Observation  equations. 

o=+o-945-  (i)f  (3)~-  {A)+  (5)-(i9)  +  (2o) 
o=-o-i58-  (2)+  (3)-  (4)+  (6)-  (7)+  (S) 
0=^-0-027-  (i)+  (2)  -  (S)+  (9)-(iS)  +  (2o) 
0=  -f  0-462-  ( 15)  +  ( 17 )  -  ( 22 )  +  ( 24)  -  -  ( 25 )  +  ( 28) 
o=-o-9S8-  (9)  +  (i3)-(i7)  +  (i8)-(2i)  +  (22) 
o=+o-32i--   (9)f(ii)-^(i5)  +  (iS)-(27)-+-(28) 

0=-0-236~(l2)-f  (l3)-(2l)  +  (23)-(29)^(30) 

o=+o-o72--(i6)  +  (iS)       (9)  +  (;i2)-(3o)  +  (3i) 

o=  +  i-026-(i5)  +  (i6)     (26)  +  (28)^-(3i)  +  (33) 

o=:-<-o-o93.-(r4)  +  (i6)-(3i)  +  (32)  -(34)-f(36) 

o=  +  i-432-(i4)-|  (iS)--   (9)  +  (io)-(35)  +  (36) 

o=~9"5  +  2-99(4) -2-12(5) -0-87(6)4-4-08(7) -5-74(8) -I -66(9) 4- 1 -49(  iSV-5-3S(  i9)-3-S9(2o) 

o=+4-2+i-56(9)-]-i4(ii)-o-42(i3)+4-S7(2i)-6-92(22)-2-o5(24)    -0-38(25^-3-75(27^ 

+4-13(28) 
o=+3-o+o-6o(9)  -4'68(  i2)-f  4-o8(i3)+8-7i(i6)    -9-58(  17  )-•  2-29^21 )     6-o5(22)-3-76u3l 

+0-871  iSi 
o=—o-8  1-0-60(9)     9'46(ii ) +8-86(1 2)4  5-32(15)     6-i9(  i6)+o-S7(  iS)  -2-5u  26)  -3-821  27) 

+  1-31(28) 
o=  +  i-44-i-57(9)-7-i3(io)  t  5'56(i2l     5-15(14)    -5-i5(  16) -i-o-oo(  iS^     0-24^30)   -1-30(31) 

+  1-54(32^ 


♦Correction  for  eccentricilv  indicated. 


t Correction  to  refer  the  old  to  the  new  stntion  of  1865. 


52 


THE    EASTERN    OBLIQUE    ARC. 


Reciprocals  of  the  iveights  or  -calues  of 


^3 


0= +0-945 
o  =  — o'i58 

0=+0'027 

o=+o'462 
0= -0-988 
o  =  +  o-32i 
o=— 0-236 
0= +0-072 
0  = +  1-026 
0= +0-093 
0=  + 1-432 

o=-9'5 
o=+4-2 

o=+3'o 
o=— 0-8 
o=  +  i-4 


C2 


0-9 

1-6 

I '4 
'•4 
07 
0-5 
0-9 

19 


9-4    +3'0    +3'3 

6-0   —I -8 

8-6 


10 

n 

12 
13 
14 
15 
16 

17 
iS 


1-2 
0-4 

0-3 
0-4 
I  'I 
0-3 
0-3 
0-4 

1-6 


19 

20 
21 
22 
22 

24 

25 
26 

27 


17 

2-1 

0-4 
0-5 
0-5 
ro 

o"3 
0-4 
0-4 


C3        C4        C5         C6 


Normal  equations. 

C7        Cg        C9       Cio        Cii 


Cn 


28 

0-3 

29 

0-3 

30 

0-4 

31 

0-4 

32 

2-8 

33 

0-3 

34 

0-9 

35 

4-9 

36 

1-2 

Cm 


C15 


-35    -35  -3'5 

—0-9    +0-6  +0-6 

5-2    +3-5    +0-8    +3-5 

4'9  +3'5    +0'6 

2-3    -0-7 

4-9    -0-7    -0-7 

2-0    +0-7 

6-7 


C,  =  — o  -4899 
Cj= +0-5886 
C3= +0-1590 
C4  =  +o  -2016 


-3'5 


+  3-5 

+3'5 


+  2-3 
11-9 


+  io-i6i 

—  12-001 
+  14-105 

—  0*770 

-  0-770 

-  0770 


—  0-770 
147-085 


+  2  964 
+6-863 
-S-540 
-0-681 
— 2-116 
-2-964 
+  1-239 


+4  920 
53 '630 


Resulting  values  of  correlates. 


C5  =  -ri  '1956 
C6  =  -o-i55o 

C7=--o-3553 
C8= -0-5471 


C 


-o  -8014 


C,o=+o-ii45 
C,i  =  --o  -2924 
C,^=+o-i348 


-  0252 

-  0-S07 

+  ■■"75 

+  0-252 

+  4-000 

-  3765 
+  2-613 
+  2-613 
+  0-252 
+  3-966 
+  26-4S7 

I02-o6l 


-  0-252 

-  1-203 
+  0-252 

-  3-207 

-  2-658 
-t-  4-767 

—  4-064 

-  1-857 

+  0-252 
+  3-966 

+  I3-'145 

-26-719 

90' 100 


C„= +0-0750 

Ci4  =  — 0-0807 
C,5  =  — 0-0361 
C,6= —0-0563 


C16 


+    2-983 

-  2-983 

-  2-983 

-  1-764- 

-  0-194 

-  1-025 

-  2-378 

-  17-204 
+  4-951 
■^  4-653 
-19-473 
+  26-132 

119-437 


Resulting  corrections  to  observed  directions. 


(l)  = 

=  +0-397 

(io)  = 

=  +0-131 

(19)  = 

=  —0  -400 

(28)  = 

=  —0-148 

Probable  error  of 

(2) 

-0  -387 

(II) 

+0  -040 

(20) 

+0  -406 

(29) 

+  0-107 

an  observed    direc- 

(3) 

+0-158 
+0  -426 
- 1  -086 

(12) 
(13) 
(14) 

-0-134 

-|-o  -192 

—  O-T23 

(21) 
(22) 
(23) 

—0  -264 
+0  -482 
-0  -329 

(30) 
(31) 
(32) 

+  0  -082 
+  0  -085 
+  0  -078 

tion. 

(4) 
(5) 

-■^"V'tT 

(6) 

^0-330 

(15) 

+  0-169 

(24) 

+  0  -355 

(33) 

—  0  -240 

" 

(7) 

~o  -019 

(16) 

-0  '099 

(25) 

—0  -069 

(34) 

-0-103 

=  ±0-34 

(8) 

-0-310 

(17) 

-0  -089 

(26) 

+0  -284 

(35) 

+  '  '433 

(9) 

+0  -266 

(18) 

+0  -226 

(27) 

+  0-005 

(36) 

—0-214 

Check: 

-VwQA 

=4-133  and  [ 

pVvl^A 

■I35- 

BASE   LINES    AND    BASE   NETS. 


53 


Ucsul/in 

if  u>i}^/('s  and  side 

sn/(/ic  /' 

iff  fslavd  base  ncl. 

No. 

Stations. 

Ob.served  angles. 

Correc- 

tioti. 

Spher- 
ical 
aiiKles. 

exceL.              I-""- 

Distances  iti 
meters. 

0 

/         // 

// 

/' 

// 

-  7+  8 

Rulaiid 

27 

J  7     02716 

0    290 

02  -426 

0  -218 

4-147  953  5 

14   058-971 

-  4+  6 

Fire  Island  East  Ba.se 

112 

32     52  425 

-0  096 

52  -329 

0  -217 

4-452   173  4 

28  325    23 

-  2+  3 

Fire  Island  West  Base 

40 

1"    05-353 

H-0  -544 

05  -897 

0-217 

4-296  291    [ 

19   782  -95 

-19+20 

West  Hills 

21 

21     45' 133 

po  -806 

45  939 

0  -296 

(•'47  953  5 

14   058-971 

■  4+  5 

Fire  Island  East  Base 

44 

48     25  •  1 29 

I  -512 

23  -617 

0296 

4  -434  543  0 

27    198-38 

-    '+  3 

Fire  Island  West  Base 

"3 

49     5 J  '571 

0-239 

51  -332 

0296 

4  -547  828  6 

35  304  -38 

-18+20 

West  Hills 

54 

43      : 6  '067 

jo  -180 

:6  -247 

0  -026 

4-452   173  4 

28  325    23 

-  8+  9 

Rnland 

51 

36     59-619 

+0  -576 

60-195 

0  -625 

4  -434  543  0 

27    198-38 

-   1+   2 

Fire  Island  West  Base 

73 

39     46-218 

-0  -783 

45  '435 

0  -626 

4-522  397  2 

33  296-39 

-1S+19 

We,st  Hills 

33 

2 1     30  '934 

-0  -626 

30  -308 

0-547 

4  -296  291    1 

19   782-95 

-  7+  9 

Rnland 

7« 

54     02  -335 

t-o  -286 

02  -62 1 

0-547 

4  -547  828  5 

35  304  -37 

-  5+  6 

Fire  Island  East  Base 

67 

44     27  -296 

(-1  -416 

28  -712 

0-547 

4  -522  397    1 

33  296-39 

■30+31 

Tashua 

3'^ 

20     42-545 

+0  -003 

42  -548 

I  -344 

4  -522  397    1 

33  296  -39 

9+12 

Ruland 

73 

59     43  '301 

—0  -400 

42  -901 

'  -345 

4  ■7>2  561    3 

51  589  50 

-16+1S 

West  Hills 

67 

39     38  -259 

+0  -325 

38  -584 

I  -344 

4  -695  847  6 

49  641  -Si 

-27-t-28 

Wooster 

29 

'S   52-587 

—0-152 

52  •4.^,5 

•  -683 

4-522  397    1 

33  296-39 

9+II 

Ruland 

6[ 

26     28  -038 

—0  -226 

27-812 

1-683 

4  -776  212   I 

59  732  -69 

15+18 

West  Hills 

89 

14     44-744 

+0  -057 

44  -<Soi 

I  -683 

4  -832  520  7 

68  001  -85 

26+27 

Wooster 

28 

53     58  -295 

—0  -280 

58  01 5 

0  -621 

4  -695  847  6 

49  641  -81 

30+33 

Tashua 

13S 

32     49 '081 

-0  -323 

48  -758 

0  -620 

4-832  520  7 

68  001  -85 

11  +  12 

Ruland 

12 

33     15  -263 

-0-174 

15-089 

0  -62 1 

4  -348  836  2 

22  327  -30 

26+28 

Wooster 

5S 

12     50-882 

—0  -432 

50  '45" 

0-959 

4-712  561  3 

51  5S9-50 

31+33 

Tashua 

100 

1 2     06  -536 

-0  -326 

06  -210 

0  -959 

4  -776  2120 

59  732  -68 

15+16 

West  Hills 

21 

35     06  -485 

-0  -268 

06  -217 

0-959 

4  -348  836  2 

22  327-30 

21+22 

Sandford 

23 

24     41  -555 

+  0-746 

42  -301 

I  -902  ; 

4  522  397   1 

33  296-39 

9  +  13 

Ruland 

101 

[9     14  -968 

-0  -074 

14  -S94 

I  -903  ! 

4-914  715  9 

82  170-49 

17  +  18 

West  Hills 

55 

16     08-196 

+0-316 

oS -512 

I  -902 

4  -838  030  8 

68  870  •  1 1 

22  +  23 

Sandford 

'9 

12     16-869 

-0  -8 1 2 

16  -057 

0  -736 

4-712  561   3 

51   589-50 

16+17 

West  Hills 

12 

23     30  -063 

+  0-OIO 

30  '073 

0-737  ' 

4  -527  058  6 

33  655  70 

29+31 

Tashua 

148 

24      16-201 

-0  -022 

16  -079 

0-736  \ 

4-914  716  0 

82   I 70  50 

21  +  23 

Sandford 

42 

36     58  -424 

0  -066 

58  -358 

1  ■317 

4-695  847  6 

49  641  -81 

12  +  13 

Ruland 

27 

19     31  -667 

4-0  -326 

31   993 

1  -318 

4  -527  058  6 

33  655  70 

29+30 

Tashua 

IK) 

03     33  "656 

—0  -024 

33  632 

1  -318 

4  -838  030  8 

68  870-11 

22  1  24 

Sandford 

45 

38     51  -567 

—0-126 

51  -44" 

2  -320 

4-776  212  0 

59  732  -68 

15+17 

West  Hills 

33 

58     36  -548 

-0  -257 

36  -291 

2  -320 

4  -669   1710 

46  684  -3 1 

25 +  28 

Wooster 

100 

22     39  -308 

-^0  -079 

39-229 

2  -321 

4-^14  716  0 

82   170  "50 

54 


THE    EASTERN    OBLIQUE    ARC. 


Resulting 

angles  and  si 

des  of  th 

c  Fire  Isl 

ind  base 

-'/;■/'— continued. 

No. 

stations. 

Observed  angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

.Spher- 
ical 
excess. 

Log.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

f  / 

-21-1-24 

Sandford 

69 

03 

33  '122 

+0  -621 

33  743 

2-540 

4  -S32  520 

7 

68  001  -85 

-II  +  I3 

Rulaiid 

39 

52 

46  -930 

-f  0-152 

47  -082 

2-540 

4  -669    1 70 

9 

46   684  -30 

25  +  27 

Wooster 

71 

03 

46721 

+  0  -074 

46  '795 

2-540 

4  '838  030 

9 

68  870-13 

23  +  24 

Sandford 

26 

26 

34  -698 

+0  -686 

35  -384 

0-592 

4  -348   S36 

2 

22   327  -30 

29-33 

Taslma 

IIT 

23 

37  '263 

+0  -348 

37-611 

0-592 

4  -669    171 

I 

46  6S4  -32 

25  ;  26 

Wooster 

42 

09 

48  -426 

+0  -355 

48  -781 

0-592 

4  '527  058 

8 

33  655-71 

34  +  35 

Bald  Hill 

62 

40 

12-852 

+ 1  -536 

14  -388 

0  -826 

4  -695  847 

6 

49  641  -81 

30+32 

Tashua 

96 

34 

59  '444 

—0  -004 

59  '440 

0   826 

4  744  375 

8 

55  510-58 

10+12 

Ruland 

20 

44 

48-915 

—0  -265 

48  -650 

0  -826 

4  '296  541 

I 

'9  794-34 

35+36 

Bald  Hill 

36 

51 

27  -977 

—  I  -646 

26-331 

I  '253 

4  '522  397 

I 

33  296-38 

9+10 

Riilaiid 

53 

14 

54  -386 

--0-I35 

54-251 

1  -253 

4  '648   135 

7 

44  477  '02 

14+18 

West  Hills 

89 

53 

42  -828 

+0  -349 

43 -'77 

1  '253 

4  744  375 

9 

55  510-60 

34+36 

Bald  Hill 

99 

31 

40  -829 

—  0  TIO 

40-719 

0  735 

4-712  561 

3 

51   589-50 

31+32 

Tashua 

58 

14 

16  -899 

—  0  -007 

16  -892 

0  735 

4 '648  135 

6 

44  477  -01 

14+16 

West  Hills 

22 

14 

04  -569 

+  0  '024 

04  -593 

0  734 

4-296  541 

3 

19  794  -35 

Deseripiions  of  base  net  stations. 

Fire  Island  West  Base,  Long  Island,  New  York.  The  ba.se  was  located  m  a  most 
in.secure  position,  close  to  the  beach  of  the  narrow  strip  of  land  known  as  Fire  Island, 
and  with  its  western  terminus  not  far  from  the  Fire  Island  Light-House.  The  locality 
is  subject  to  total  changes  of  aspect,  dvte  to  drifting  .sands  and  inundations  and  erosions 
from  high  tides.  This  being  well  known,  Superintendent  Ha.ss]er  connected  it  directly 
with  the  line  Ruland-We.st  Hills,  which  he  called  his  ' '  Mountain  ba.se. ' '  This  connec- 
tion was  made  by  means  of  a  quadrilateral  of  which  all  angles  were  measured. 

It  appears  that  the  .station  was  originally  marked  by  a  red  sand,stone  post,  with 
cro.ss  lines  upon  its  upper  surface. 

It  has  l:)een  reported  that  the  station  is  destroyed. 

Fire  Island  East  Base,  Long  Island,  New  York.  This  end  of  the  base  of  1834  was 
subjected  to  the  .same  physical  conditions  of  exposure  which  rendered  the  opposite  end 
insecure.      It  was  originally  marked  with  a  stone  post. 

Nothing  is  known  as  to  the  date  when  the  station  succumbed  to  the  destructive 
influences  .surrounding  it. 

Ruland,  vSuffolk  County,  New  York.  This  station  was  located  by  Superintendent 
Hassler  in  1833,  on  Rulands  hill,  in  Smithtown,  Long  Island,  about  halfway  between 
the  northern  and  southern  turnpike  at  Patchogue.  It  is  on  the  highest  hill  in  the 
neighborhood.  The  point  is  on  the  summit  (about  20  feet  in  diameter),  the  ground 
sloping  down  all  around  the  station.  It  was  marked  b}'  a  stoneware  crock,  with  its  top 
16  inches  below  the  surface.  Oyster  shells  are  .scattered  aboitt  the  place  to  assist  in 
finding  it.      In  1837  the  station  was  found  in  good  condition. 

The    place  was  visited    by  A.ssistant  C.  O.  Boutelle  in  i860,  who  re-marked  the 


¥ 


I 


BASE    LINES    AND    BASE    NETS.  55 

station  for  greater  security.  Four  stone  posts  were  placed  to  the  north,  soutli,  east,  and 
west  of  the  center  stone  post.  On  the  upper  surface  of  th'j  center  stone  post  the  inter- 
section of  two  lines  marks  the  position  (jf  the  center  point  of  llie  Hassler  crock  of  1S33. 
Around  each  post  concrete  was  placed  to  .secure  it  firndy  in  jxjsition.  Upon  the 
center  stone  was  placed  a  .stout  stub  of  locust  wood  into  the  toj)  of  which,  level  with 
the  ground,  a  copper  tack  was  dri\en,  marking  the  center  point.  A  fuller  description 
is  given  in  the  I'ecord  of  1865,  when  the  station  was  reoccupied. 

IVes^  Hills,  vSuffolk  County,  New  Y(jrk.  This  station  was  estat)lished  Ijy  .Superin- 
tendent Ha.ssler  in  1836.  It  is  marked  l)y  a  red  sarrdstone  post,  4  feet  high  and  i 
foot  square,  strnk  in  the  ground,  with  stones  well  packed  around  it;  the  intersection  of 
diagonal  cross  lines  upon  the  lop  marks  the  .station  poiirt.  A  crock,  which  had  before 
served  as  statioir  nrark,  was  placed  upon  the  post  and  a  nail  in  a  wooden  peg  dri\-en  cen- 
trally through  it  marks  the  station.  Upon  the  side  of  the  post  facing  Harrow  were  cut 
the  initials  U.  vS.  C.  vS. 

The  station  was  reoccupied  in  1865,  and  again  described. 

The  place  is  4  miles  from  Huntington  and  7  miles  front  Farmingdale  railroad  sta- 
tioir. The  poiirt  is  on  the  stinrmit  of  a  hill.  An  exanrination  had  been  made  in  i860, 
when  the  .stone  post  appeared  not  to  have  been  disturbed,  but  the  crock  was  broken  and 
the  .stub  decayed. 

To  mark  the  point  nrore  securely,  posts  arranged  abcnit  the  center  po.st,  north,  soutli, 
east,  and  west  of  the  station,  were  sunk  to  a  level  with  the  surface  of  the  grotrnd.  A 
stout  woodeir  .stub,  with  a  nail  driven  irrto  it,  was  placed  over  the  center  of  the  old  post 
to  rrrark  the  station.      Some  further  remarks  are  giveir  iir  the  1865  description. 

Tashua,  Fairfield  County,  Conrrecticirt.  This  station  is  located  in  Trumbirll  town- 
-ship,  Fairfield  Coiurty,  Connecticut.  It  was  established  and  occtrpied  by  .Superintendent 
Hassler  in  1833.  The  station  was  reoccupied  in  1S63  by  the  party  of  Superintendent 
Bache,  by  whom  the  foUowirrg  description  is  given: 

"  The  .station  poirrt  is  marked  by  a  copper  bolt  inserted  in  the  top  of  a  granite  post 
sunk  2  feet  below  the  surface  of  the  ground.  Four  similar  posts,  8  inclres  square  and 
23^  feet  in  length,  were  adju.sted  6  feet  di.stant  to  the  rrortlr,  east,  soirtli,  and  we.st  of 
the  center  point.  The  tops  of  the  po.sts  are  marked  by  two  lines  intersecting  at  right 
angles  and  the  letter's  U.  S.  C.  S.  Four  directions  to  .signals  visible  front  tire  station 
are  marked  by  copper  tacks  driveir  into  hickory  stubs  at  distances  171  feet  3  inches 
toward  Ruland,  121  feet  7  inclres  toward  West  Hills,  73  feet  q  inches  toward  \\'oo.ster, 
and  70  feet  3  inches  toward  tower  in  Warren." 

Sandford,  New  Haven  County,  Connecticut,  1862.  This  geodetic  point  is  located 
on  the  highest  and  most  western  summit  of  Sandford  Motintairr,  5  feet  from  a  pile 
of  stones  which  marks  the  Iroundry  line  between  New  Haven  and  Bethany  townships. 
The  poiirt  is  marked  by  the  center  of  a  half-inch  drill  hole  in  the  top  of  a  granite  post 
which  is  2)^  feet  in  length  and  i  foot  .square  at  the  upper  surface.  Two  cro.ss  lines 
and  the  letters  U.  vS.  C.  S.  ar'e  cut  on  its  top,  which  is  i  ^j  feet  below  the  general  surface 
of  the  ground.  For  greater  security  fiuir  granite  po.sts,  each  2^2  feet  long  and  6  inches 
squar'e  at  the  top,  wei'e  sunk  into  the  gr'ound  at  points  about  6  feet  to  the  north,  east, 
south,  and  west  of  the  station.  The  tops  of  these  posts  were  tlush  with  the  ground. 
To  this  description  A.ssistant  G.  W.  Dean  adds  the  following:  "  The  topof  the  stone  jiost 
marking  the  station  was  sunk  20  inches  below  the  plane  of  the  four  surrounding  ,-<toues. 


56  THE    EASTERN    OBLIQUE    ARC. 

A  copper  bolt  was  driven  into  the  central  stone  and  the  center  accurately  marked  by 
intersecting  lines.  A  cedar  stub  was  placed  immediately  over  the  center  of  the  granite 
post,  the  top  of  which  was  flush  with  the  ground  and  firmly  secured  with  earth.  The 
station  point  was  further  marked  by  a  composition  nail  driven  into  the  tO]i  of  the  cedar 
stub. ' ' 

Bald  Hill ,  P'airfield  County,  Connecticut.  This  .station  was  estalilished  in  1833  by 
Superintendent  Hassler  and  occuj^ied  by  him  in  that  year. 

The  hill  is  situated  in  Wilton  Township,  about  4  miles  .south  of  Ridgefield.  The 
station  was  visited  b>'  Assistant  Farley  in  1868,  who  found  fragments  of  an  earthenware 
crock  (of  the  pattern  of  the  Hassler  crocks,  or  cones,  as  he  called  them),  and  marks  cut 
on  three  rocks,  but  he  was  not  able  to  identify  the  marks  owing  to  the  (apparent )  loss  of 
the  original  description  of  the  station  by  vSuperintendent  Hassler  and  by  As.sistant  Blunt 
in  i.s6ri.  Wliat  made  the  search  at  the  place  more  difficult  was  the  fact  that  rock  blasting- 
had  Ijcen  going  on  there  for  .some  time.  A  second  visit  in  1869  elicited  no  certain 
information  from  want  of  application  of  proper  means.  The  place  was  next  examined 
1)\'  Assistant  G.  Bradford  in  1882  and  1SS4,  when,  1)}-  means  of  the  determination  of  a 
temporary  signal,  the  location  of  the  crock  (cone)  placed  bj'  Assistant  Blunt  in  1866 
was  readily  discovered.  It  is  a.ssunied  that  this  crock  occupies  the  position  of  the 
Hassler  crock,  because  A.ssistant  Blunt  is  said  to  have  put  it  in  the  place  of  the  fragments 
of  the  older  one.      The  station  appears  to  have  been  recovered. 

]\\iostci\  Fairfield  County,  Connecticut.  This  station  was  e.stal)lished  in  1864  by 
the  party  of  vSuperintendent  Bache.  It  is  located  in  Ridgefield  Township,  about  4  miles 
.southwest  of  Danbury,  on  Wooster  Mountain,  known  to  the  residents  in  the  vicinity  as 
Pine  Hill. 

The  station  point  is  marked  b}'  a  copper  bolt,  and  is  located  on  the  highest  point 
of  gneiss  which  crops  out  near  the  summit  of  the  mountain.  The  top  of  the  ledge  is 
quite  limited,  its  length  east  and  west  being  about  25  feet. 

4.    THK    KENT    ISLAND    BA.SK    LINE,    BASE    NET    AND    EXTEN.SION,   JNLVRVLAND,    1 844. 
Louitioit .  iiHasiD'inuiit .  iDid  rcsu/fiiig  Ic/igjh  of  ^'^^  Kent  Island  base  line,  Maryland,  /S/^. 

Kent  Island,  in  Queen  Anne  County,  Maryland,  on  the  western  shore  of  which  the 
base  was  measured,  is  situated  on  the  east  .side  of  Chesapeake  Bay,  and  is  nearly  oppo- 
.site  Annapolis  Harl>or.  Originally  it  was  intended  as  a  check  on  the  main  triangvilation 
which  extended  from  the  Fire  Island  ba.se  .southward  and  westward,  but  its  po.sition  near 
the  latitude  of  39"  rendered  it  desirable  to  incorporate  it  in  the  ea.stern  part  of  the 
transcontinental  triangulation. 

An  account  of  the  measure  and  length  of  this  base  is  contained  in  the  Coast  Survey 
Report  for  the  year  1866,  supplement  to  Appendix  No.  8,  page  140,  and  again  in 
Special  Publication  No.  4,  "The  Transcontinental  Triangulation." 

The  middle  point  of  the  Ijase  is  in  latitude  38°  56'' i,  and  in  longitude  76°  2i''2,  the 
mean  a/.inuith  is  14°  35''4,  and  the  length  87  kilometers  (or  5'4  statute  miles).  The 
surface  of  this  part  of  the  i.sland  is  slightly  undulating,  and  the  line  crosses  cultivated 
fields,  with  some  portions  covered  by  swamps  and  woods.  The  elevation  is  verj-  little 
above  the  surface  of  the  bay.  The  shore  is  subject  to  erosion,  in  consequence  of  which 
the  terminal  monuments,  each  consisting  of  an  upright  .stone  surface  mark  with  a  copper 


BASE    LINES    AND    HASE    NETS.  57 

bolt  in  a  piece  of  slate  below  the  surface,  the  whole  being  protected  by  nibble  masonry, 
have  disappeared. 

The  base  was  measured  I)}'  Assistant  J.  Ferguson,  in  .Ma\'  aiul  June,  1844.  by 
means  of  the  same  apparatus  as  was  used  for  the  measure  of  the  Fire  Island  base  ten 
years  before.  It  is  known  as  the  Hasslerba.se  apparatus,*  and  consists  oi  four  rectangu- 
lar iron  bars  eacli  2  meters  long,  put  together  endwise  and  aligned  in  a  wooden  trough. 

The  protruding  ends  of  this  S-meter  1)ar  ha\-e  semicircular  notches     f  ' ■'™^      acnws 

which  was   stretched  a   spider   thread;    over    this   was    mounted,      f  '^     on   an 

independent  stand,  an  adjustaljle  micrometer  microscope,  b\-  means  of  which  tlie  mea.sure 
was  held  while  the  l)ar  was  brought  forward  into  a  new  position.  All  needed  adjust- 
ments for  the  apparatus  were  provided  for  and  the  temperature  of  the  bar  was  read  from 
thermometers  attached  to  the  top  of  the  2-meter  bars  placed  in  the  liottom  of  the  trough, 
1;  which  is  .supposed  to  have  been  covered  with  canvas.      At  the  end  oi  a  day's  work  or 

at  other  times  when  neces.sary,  the  end  of  the  last  bar  laid  was  transferred  to  the  ground, 
generally  by  a  plummet.  Only  one  measure  was  made,  and  the  total  time  cf)nsumed 
was  a  little  over  one  month. 

The  four  2-meter  bars  made  by  Troughton,  of  London,  about  18 13  were  standardized 
in  1817  by  Hassler,  by  using  the  Committee  Meter,  in  1834-35  by  using  the  Troughton 
bra.ss  .scale,  and  finally,  in  1844-45,  b}'  Superintendent  Bache.  J.  Sa.xton,  and  \V. 
Wiirdemann,  by  u.sing  a  Bessel  comparator,  with  the  following  results: 


111  ISI7 

■2'  =  7""999  9506  at  0°  C 

1834-35 

S  'ooo  0414 

1835 

t7-999  9764 

IS44-45 

7-999  S716 

±  5,5 

This  last  value,  after  verification  in  July,  1854,  was  finally  adopted  for  the  two  bases 
measured  with  this  apparatus  in  1S44.  The  coefficient  of  expansion  of  the  bar  which 
was  determined  in  18 17  by  Ha.ssler  at  Newark,  viz,  o'ooo  012  534  for  the  centigrade 
scale,  was  adopted  and,  though  somewhat  large,  may  nevertheless  be  true  for  these 
particular  bars,  now  lost.  The  mean  temperature  of  the  bar  during  measurement  of  the 
base  was  25°"i8  C.  (or  77°'33  F.).      The  deduced  length  of  the  base  is  as  follows: 

I  0S6  boxes  .S6S7"'-,S6o6 

Excess  of  last  box  over  end  mark  at  South  Rase,  as  measured  b%-  Bar  D  and  .scaK-  2  '0508 

Correction  for  excess  (25°  44  C.)  of  temperature  of  bars  over  0°  C.  and  graduation  error  of 

thermometers  (  — o°'255  C.  )  -2  7424 

Correction  for  inclination  of  boxes  1  \xx17 

Redviction  to  half-tide  level  of  bay  for  surface  elevation  and  height  of  boxes  5"''o  — 0*0069 


Resulting  length  of  base  S6S7"'5446 

The  probal)le  error  of  this  value  can  (ml\-  be  estimated,  since  the  base  was  meas- 
ured but  once.  Supposing  the  combined  length  of  the  four  2-meter  bars  subject  to 
±20/i,  the  effect  on  the  ba.se  will  be  ±o"'"o22;  an  assiuned  error  of   ±5',,    part   in  the 

*Kor  a  description,  with  illustrations,  of  the  apparatus,  seethe  Transactions  of  the  .\raerican  Philosophicil  Society, 
Philadelphia,    Pennsylvania,   for  the  year  iSj5,   pp.   27,viJ*fi.     ."^ee  also  the  preceding:  account  of    the  I'irc  Island  Ivase 

nieasnrotuent, 

tRes\iU  of  coniparison>.  uuule  :ifter  cleanitii;  two  of  the  J-iueler  hats  which  were  louiul  ruslv  when  examined. 


58 


THK    EASTERN    OBLIQUE    ARC. 


coefficient  of  expansion  would  produce  dr  o'""055;  again,  the  effect  for  imperfect  tempera- 
ture correction,  for  inequality  in  number  of  boxes  laid  with  rising  and  with  falling 
temperatures,  may  be  taken  as  d=o"''034;  other  minor  uncertainties  may  be  omitted. 
Combining  the  several  values  for  probable  error  gives  zho'"'o68,  equal  to  27^00  of  the 
length  nearh'.  This  ma}'  be  taken  to  represent  the  measuring  error,  and  to  include  the 
probable  error  due  to  our  practical  unit  of  length,  the  Committee  Meter,  taken  as  ±  Hm- 
Resulting    length    of   Kent    Island    base,    S  687'5446    meters    and    its    logarithm, 

±■0680 
3-938  8 97  05 

±3  40 

A'(7//  Is/aitd  /hisr  net  and  restills  of  adjiisluutii. 

The  following  abstracts  of  observed  and  adjusted  directions  at  the  nine  stations  form- 
ing the  base  net  proper,  as  well  as  the  conditional  equations  and  results  of  its  adjustment 
with  resulting  length  of  triangle  sides,  were  copied  from  Part  I,  Special  Publication  No.  4, 
"  The  Transcontinental  Triangulation,"  and  from  Part  III  of  the  same  publication  the 
results  of  two  triangles  *  to  the  northward  of  the  net  and  of  35  triangles  to  the  westward 
and  southward  of  the  base.t  The  triangles  of  this  last  extension  are  shown  on  the  foUow- 
inof  sketch: 


OsbornesRuirt 


Finlay 


Kent  Island  North  Base 


Kent  Island  South  Base 


Marriott 


Kilometers 


Statute  Miles 


10 


*  Shown  on  the  above  sketch  by  dotted  lines. 

tFor  adjustment  of  this  work  see  Special  Publication  No.  4,    ■  The  Transcontinental  Triangulation.' 


BASE    LINES    AND    BASE    NETS.  59 

The  heights  of  the  stations  above  the  half-tide  level  of  the  ocean  are  small  and 
approximately  as  follows: 


Meiers 

Kent  Island  North  Base 

5 

Kent  Island  South  Base 

5 

Taylor 

29 

Marriott 

76 

Linstid 

48 

Webb 

72 

Swan 

8 

Pooles  Island 

4 

Finlay 

150 

Osbornes  Ruin 

90 

Turkey  Point 

25 

f  stations  along  the  Blue  K 

Meters. 

Hill 

84    ■ 

Soper 

143 

Stabler 

174 

Peach  Grove 

159 

Sugar  Loaf 

390 

Maryland  Heights 

444 

Bull  Run 

419 

Mount  Marshall 

028 

Fork 

174 

Clark 

334 

Humpback                        i 

no 

Spear 

492 

Tobacco  Row 

895 

No  corrections  to  the  observed  horizontal  directions  on  account  of  altitude  were 
applied,  as  they  are  too  small  in  comparison  with  the  angular  corrections  required  by  the 
net  adjustment  to  be  considered.  In  latitude  39°  the  correction  to  a  direction  for  height 
of  station  sighted  becomes  o"'ooo  066  sin  2  c^./i,  hence  the  maxinunn  correction  would 
still  be  le.ss  than  o""o8,  whereas  the  net  adjustment  in  this  region  in  several  instances 
calls  for  angular  corrections  exceeding  i". 

The  results  of  the  triangle  side  computations  between  the  Kent  Island  and  the 
Atlanta  base  lines,  published  in  Coa,st  and  Geodetic  Survey  Report  for  1878,  pages  94-1 12, 
are  now  superseded.  A  portion  of  this  work  was  readjusted  in  reditcing  the  tran.sconti- 
nental  triangulation  and  the  results  are  reproduced  in  this  publication. 


J 


6o 


THE    EASTERN    OBLIQUE    ARC. 


Adsfraiis  of  rcsii/tiia;-  horizontal  directions,  observed  and  adjusted,  at  tlie  stations  foDuing  the'Jbase 

net,  i844-i8gj. 

Kent  Island  South  Base,  Queen  Anne  County,  Maryland.  May  30  to  June  4,  1S47.  30""  repeating 
theodolite  No.  u.  E.  Blunt,  ob.server.  (Observations  in  1.S44  by  J.  Ferguson  superseded  by 
above. ) 


Number  of 
directions. 

Object  observed. 

Resulting  direc- 
tions from  sta- 
tion adjustment. 

Corrections  from 
base  net  adjust- 
ment. 

Final 
seconds 

0        /          // 

// 

// 

I 

Marriott 

0     00     00  '00 

+  0-03 

00-03 

2 

Taylor 

5S     53     46  -24 

+o'o6 

46-30 

3 

Kent  Island  North  Base 

III      41       tS -25 

— 0  '09 

iS-i6 

Probable  error  of  a  single  oVjservation  of  a  direction  ( 6  D.  and  6  R. 


•69. 


Kent  /stand  North  Base,  Queen  Anne  Count}',  Maryland.  May  21  to  28,  1847.  30*^'"  repeating 
theodolite  No.  11.  E.  Blunt,  observer.  (Observations  in  i844-'45  by  J.  Fergu.son  superseded  by- 
above.  ) 


4 

Kent  Island  vSouth  Base                              0     00 

00  -oo 

+0-19 

00-19 

5 

Marriott                                                         50    05 

"5  -36 

-0-47 

04  -89. 

6 

Taylor                                                             88     35 

36 '91 

—0  -12 

36-79 

7 

Linstid                                                          121     02 

04  -33 

+0-16 

04-49 

S 

Swan  Point                                                  iSi     09 

45 '47 

+0-24 

45  -71 

Probable  error  of  a  single  observation  of  a  direction  (6/?. 

and  6  y?. ) ,  Ci  = 

±0" 

-68. 

Swan  Point,  Kent  County,   Maryland.     October   16  to   21,  1848. 

30^'" 

repeating 

theodolite  No. 

E. 

Blunt,  ob.server.      ( Oliservations  in  1845  by  J.  Ferg 

0       / 

uson  superseded  by  above. ) 
//                              // 
00  -00                     —0  -23 

// 

34 

Kent  Island  North  Base                               0     00 

59-77 

35 

Einstid                                                         56    oS 

57 '92 

+0-52 

58-44 

36 

Pooles  Island                                            169     16 

25  "5' 

—0-29 

25-22 

Probable  error  of  a  single  observation  of  a  direction  (6  D 

.  and  6  A'.  ) ,  e^  - 

=  ±1" 

■35- 

Taytor 

Anne  Arundel   County,   Maryland.     June  8  to   i( 

5,  1S47. 

jQCra 

repeating 

theodolite   No. 

E. 

Blunt,  observer.      (Observations  in  1844  by  J.  P'erg 

uson  superseded  by  above. ) 

0       / 

// 

// 

// 

10 

Kent  Island  North  Base                              0     00 

00-00 

+  0-36 

00-36 

II 

Kent  Island  South  Base                           38    36 

52-37 

-0-23 

52-14 

12 

Marriott                                                        "9     32 

44-32 

+0-53 

44  -85 

9 

Linstid                                                       247     12 

54-29 

-0-66 

53  -63 

Probable  error  of  a  single  observation  of  a  direction  ( 6  D. 

and  6  R.),  e,= 

±0" 

66. 

Pooles 

/stand,  Harford  County,  Maryland.     May   17  to  27,  184S. 

30- 

'  repeating 

theodolite  No. 

E. 

Blunt,  observer.      (Observations  in  1845  by  J.  F'erg 

uson  superseded  by  abov 

e.) 

0       / 

// 

// 

// 

31 

Swan  Point                                                      0     00 

00  -00 

+0-30 

00  -30 

32 

Linstid                                                             36     22 

15 '13 

+0-I7 

15-30 

33 

Finlay                                                               116     06 
Osbonies  Ruin                                            170     34 
Turkey  Point                                              225     05 

54-92 
06-56 
01  -56 

-0-47 

54-45 

Probable  error  of  a  single  observation  of  a  direction  (6  D.  and  6  A'.  ),  t'l  =  iho'^-69. 


BASE   LINES   AND    BASE   NETS. 


6l 


Abstracts  of  rcsnttiiii^  /lorirjoiila!  directions,  observed  and  adjusted,  at  the  stations  foniiini;  the  Imse 

net,  /8.pf-/8g7 — continued. 

Webb,  Anne  Arundel  County,  Maryland.  July  lo  to  August  14,  1848.  60  "'  direction  theodolite  No.  2. 
A.  D.  Bache,  observer.  October  21  to  December  2,  1850.  75  "'  direction  theodolite  No.  I.  A.  D. 
Bache,  observer.  September  18  to  25,  1868.  75^^'"  direction  theodolite  No.  i.  CO.  Boutelle, 
observer. 


Number  of 
directions. 

Object  observed. 

26 

Ivinstid 

27 

Marriott 

Hill 

Soper 

Stabler 

Azimuth  Mark 

25 

Finlay 

Resulting  direc- 
tions from  sta- 
tion ;idjustnient. 

Corrections  from 
base  net  adjust- 
ment. 

Final 
.seconds 

0 

/ 

'/ 

// 

//■ 

0 

fXJ 

00  -oo 

—  n  02 

59 -g^ 

76 

16 

06  19 

+  025 

06  44 

129 

26 

S'^i  -53 

0  "OO* 

5«-53 

178 

32 

04  72 

0  'CO* 

0472 

1 86 

55 

II  -56 

—0  02  * 

I'  '54 

275 

40 

01  -37 

2S9 

44 

43 'oi 

-0-23 

42  78 

Probable  error  of  a  single  observation  of  a  direction  (D.  and  7?. ),  r, 
Number  of  positions  of  circle  in  1848,  XXXIII;  in  1850  and  1868,  V. 


■94- 


Marriott,  Anne  Arundel  County,   Maryland, 
theodolite  No.   11.     E.  Blunt,  observer. 
No.  2.     A.  D.  Bache,  observer. 


November   18  to  December  9,  1846.       30"'  repeating 
May   18  to  June  18,   1S49.      60"^'"  direction  theodolite 


o  00  00  'OO 

32  06  10 '36 

70  oS  37  "17 

82  23  48  -68 

107  33  48  -30 

125  56  32-84 

147  53  16 -80 

166       06       54  '12 

Probable  error  of  a  single  observation  of  a  direction  (6  D.  and  6  R.)  in   1S46,  d  =zti  o"'67  and  of 
a  direction  (D.  and  R.)  in  1849,  <^i  =±  i"'io.     Number  of  positions  of  circle,  XI. 

Linstid,  Anne  Aritndel  County,  Maryland.  May  24  to  June  26,  184S.  60""  direction  theodolite 
No.  2.  A.  D.  Bache,  observer.  January  8  to  31,  1S97.  30'^"'  repeating  theodolite  No.  16. 
F.  \V.  Perkins  and  W.  B.  Fairfield,  observers.  Telescope  elevated  above  ground  27 '89  meters. 
(Ob.servations  in  1844-45  by  J.  Ferguson  sttpenseded  by  above.) 


Hill 

Soper 

13 

Webb 

Azinmth  Mark 

14 

Linstid 

15 

Taylor 

16 

Kent  Island  North  Base 

17 

Kent  Island  South  Base 

— 029* 

59  "71 

+0-38* 

1074 

—0-24 

36  93 

+0-34 

48-64 

—  0  '20 

32-64 

—  0  '10 

16-70 

+0-19 

54-31 

+0  -70 

— o-iS 

—0-52 

— o  -26 
+0-75 
—0-50 
-fo  02 

Probable  error  of  a  .single  observation  of  a  direction  \^D.  and  A\)  in  1S4S,  j-,  = 
a  direction  (6  D.  and  6  R. )  in  1S97,  <■,  =  ±o''''-73. 

Number  of  positions  of  circle,  XVII. 


iS 

Finlay 

19 

Pooles  Island 

Clough 

20 

Swan  Point 

Hope 

21 

Kent  Island  North  Base 

22 

Taylor 

23 

Marriott 

24 

Webb 

0 

00 

00  -QO 

46 

42 

57  -73 

69 

13 

07  -73 

77 

13 

16-97 

102 

07 

23  -lo 

140 

56 

37  -6o 

175 

43 

02  -43 

209 

40 

1 1  -28 

275 

5S 

53  -59 

00 

-70 

57 

•55 

16 

-45 

37 

■34 

03 

iS 

10 

•7S 

53 

61 

"12 

and 

of 

*  From  adjustment  of  Kent   Ishuid  extension. 


62 


THE   EASTERN   OBLIQUE    ARC. 


Abstracts  of  rcsultim::  horizontal  directions,  observed  and  adjusted,  at  the  stations  forming  the  base 

net,  1844-iSgj — continued. 

Fin  lay,  Baltimore  Count}-,  Maryland.  August  29  to  September  11,  1844.  60""  direction  theodolite 
No.  2.  J.  Ferguson,  observer.  October  15  to  December  27,  1896.  30'^"'  repeating  theodolite 
No.  16.     G.  A.  Fairfield,  observer.     Telescope  above  ground  i'5  meters. 


Number  of 
directions. 

object  ob.served 

Osbornes  Ruin 

Still  Pond 

28 

Pooles  Island 

C  lough 

29 

Linstid 

,lO 

Webb 

Resulting  direc- 
tions from  sta- 
tion adjustment. 


Corrections  from 
base  net  adjust- 
ment. 


Final 
seconds. 


/ 


CO  '00 

34-15 
20-93 


o    00 

30   48 
48   03 

55     23 

ID  I       36      01  -26 
127       19      37  -46 

Probable  error  of  a  single  ob,servation  of  a  direction  [D.  and  J\. )  in  1844,  t',  =±  i"'52  and  of  a 
direction  (6  D.  and  6  R.  )  in  1S96,  c,  =zto"-65.     Number  <if  positions  of  circle  in  1S44,  VI. 


+0-48 

—0-72 

-fo-25 


34-63 
00-54 

37 '7' 


I 

0 

II 

0 

III 

0 

IV 

0 

V 

0 

VI 

0 

VII 

0 

^'III 

0 

IX 

0 

X 

0 

XI 

0 

XII 

0 

XIII 


BASE    NP:T    ADJUSTMENT;     MARRIOTT   TO    FINLAV. 

Obserz'ation  equations. 

:4-ro5-(2)-f(3)-(4)  +  (6)-(io)  +  (ii) 
=  ~o-62-(5)  +  (6)^(io)  +  (i2)-(i5)  +  (i6) 

=  +o-49-(i)  +  (3)-(4)  +  (5)-(i6)  +  (i7) 
=  -2-3i-(6)  +  (7)-(9)  +  (io)-(2i)  f- (22) 
=  +2-97-!.(9)-(i2)-(i4)  +  (i5)--(22)-f(23) 
=  -i-37-(i3)  +  (i4)~(23)  +  (24)-(26)  +  (27) 
=  -I-87+(I8)-(24)-(25)  +  (26)-(29)^-(3o) 
=  -f2-73-(i8)  +  (i9)-(28)  +  (29)-(32)  +  (33) 
H-i-26-(i9)  +  (2o)-(3i)  +  (32)-(35)  +  (36) 

=  -i-o7-(7)  +  (8)-(2o)  +  (2i)-(34)  +  (35) 

=  ^39+i7-i(4)-i7"6(5)+o-5(6)  +  26-4(io)-29-8(ii)+3-4(i2)-f  24-91  i5)-63-9(i6)  +  39-o(  17) 

=  -f3i  +  26-4(5)-59-5(6)+33"i(7)+63-4(i4)-ii5-6(i5)  +  52-2(i6)J-30-3(2i)-6r-6(22) 

+3i'3(23) 
=  -28+7-3(5)  -r9-4(7)  +  i2-i(8)  +  27-5(i3)-52-3(i4)H  24-8(16) +7-6(25)- 12-7(26) 

+5-1(27)+  i5-5(28)-59-2(29)+43-7(3o)  +  28-6(3i)-32-4(32)+3-8(33)  +  i4-2(34)-5-2(35) 

-9-0(36) 


l^ILL- 


BASE   LINES    AND    BASE   NETS.  63 

The  correlate  and  normal  equations,  when  established  and  solved,  K'lve  the  follow- 
ing values  of  corrections  to  the  angular  directions: 

//  //  //  // 

(i)= +0-0310        (10)= +0-359  9        (19)=  -0-184  9  (28)=  -^0-475  .S 

(2)  +0-0597         (ri)       -0-2322         (20)      -- 0-5 1. So  (29)      —0-7247 

(3)  —00907         (12)      40-5291         (21)      —0-2645  (30)      J-0-2490 

(4)  +0-1897         (13)      -0-2394         (22)      +0-7474  (31)      +0-2957 

(5)  —0-4716         (14)       I   0-341    I         (23)      —0-4996  (32)      +0-1730 

(6)  —0-1167         (15)  0-1954         (24)      +o-or6  6  (33)      —0-4687 

(7)  +0-164  2         (16)  o'loi   2         (25)      —0-230  I  (34)      -0-227  6 

(8)  +0-2373         {17)      +0-1948         (26)      -0-0213  (35)      +0-5161 

(9)  -0-6568         (18)      +0-7030         (27)      +0-2514  (361      -0-2885 

Checks:  vSum  of    |-  corrections  55  -35  and  2i  pvzi  =  +  4-867 
Sum  of  —  corrections  55  -32     —  2  rcC  =   -•-  4  '872 

Mean  error  of  an  observed  direction  /«,  =   /[/>?';']  _  j^  o"-6i   where  ti  =  number  of  conditions. 

*       n 

Mean  error  of  an  auj^^le  in ,c  =  in,  ^/^  =  ±  o"  -87  and  probable  error  of  the  same  ±:  (/'  -59. 

EXTENSION    OF   THE    KENT    ISLAND    BASE    NET    TO    THE    NORTHWARD. 

Abstracts  of  rcsitltiiii;-  hoi  izontal  directions,  observed  and  adjusted  at  stations  to  tlic  north  of  the  net. 

Osbornes  Ruin,  Harford  Count)-,  Maryland.  September  23  to  October  2,  1844.  60""  direction  theod- 
olite No.  2.  J.  Ferguson,  observer.  August  17  to  September  20,  1896.  30*^'"  repeating;  theod- 
olite No.  16.     G.  A.  Fairfield,  observer.     Telescope  14-17  meters  above  ground  in  1S96. 

O  /  //  //  // 

Turkey  Point  o  00  00-00  +0-11  00 'ii 

Pooles  Island  81  27  17-53  — o '06  1747 

Finlay  158  56  33  29  —0-09  33  20 

Principio  324  49  48  33                    

Probable  error  of  a  single  observation  of  a  direction  (/'>.  and  R.)  in  1S44,  t',  ==  i"'33  and  of  a 
direction  (6  D.  and  6  R.)  in  1896,  <■,  =4ro"-35.     Number  of  positions  of  circle  in  1844,  VI. 

Turlzcy  Point,  Cecil  County,  Mar3-land.  May  31  to  June  17,  1S45.  60*^'"  direction  theodolite  No.  2. 
J.  Ferguson,  observer.  September  30  to  October  19,  1896.  35""  direction  theodolite  No.  10. 
J.  Nelson,  observer.     Telescope  2-08  meters  above  ground  in  1896. 

o  /  //  //  // 

Pooles  Island 
Osbornes  Ruin 
Principio 

Probable  error  of  a  single  observation   of  a  direction  i^/^.  and  A'.)  in  1S45,  <•,  =2=  i"-49  and  of 
a  direction  in  1896,  c,  =rto"-62. 

Number  of  positions  of  circle  in  1845,  VI;  and  in  1896,  XII. 


0 

00 

00  "OO 

+065 

0065 

44 

01 

48  -72 

—0-44 

4S-2S 

131 

14 

41  -24 

.... 

64  THE   EASTERN   OBLIQUE   ARC. 

Abstracts  of  resulting  horizontal  directions  observed  and  adjusted  at  stations  forming  the  extension  of 
the  Kent  Island  base  net  to  the  zuesliuard  and  southward. 

Hill,  Prince  George  Count}',  Maryland.  June  i8  to  July  15,  1S46.  60-"'  direction  theodolite  No.  2. 
A.  D.  Bache,  observer.  August  8  to  October  4,  1850.  75-'"  direction  theodolite  No.  r.  A.  D. 
Bache  and  A.  A.  Humphrey.?,  ob,servers.  October  9  to  November  12,  186S.  75'^^'"  direction 
theodolite.  No.  i.     CO.  Boutelle,  observer.      Telescope  1676  meters  above  ground  in  1868. 


Do. .It      fi   „„i  i^orrecnon  irom  ,.•      , 

Objects  observed.  ReM.ltsofloc.il  figure  adjust  ^••"■' 

•'  aojiistment.  *=  „,<>„t  seconds 


-f  0  '10 

42-57 

+  0  '20 

57  70 

-0-31 

40  -40 

Peach  Grove  o  00  00  'oo                  — o  '30                  59  70 

Causten  5  54  28 '96 

"Sugar  Loaf  37  48  42-47 

Stabler  65  16  57 '50 

Soper  69  14  4071 

Azinuith  Mark  125  08  23  "97 

Webb  125  oS  24-12                   +0-I2                   24-24 

Marriott  iSi  48  56-12                   +0-20                   56-32 

Probable  error  of  a  single  observation  of  a  direction  (/•'.and  /\'.),et=  =ho''-90.     Number  of  positions 
of  circle  in  1846  and  1850,  V:  in  1S68,  VII. 

Soper,  Montgomery  County,  Maryland.     June  19  to  July  23,   1850.     75*^"'  direction  theodolite  No.  i. 

A.  D.  Bache,  observer. 

o  /  //  /,  // 

Webb  o    00    00  -00  — o  '08 

:Marriott  39     41     37 '08  — 0-17 

Hill  75     01      10-92  +0-24 

.Azimuth  Mark 
Cau.sten 

Stabler  233     17      ....  09-98 

Probable  error  of  a  single  ob.servation  of  a  direction  (  /).  and  A'.  ),<;',=  zto^'-gi.     Number  of  positions 
of  circle,  V. 

Stabler,   Montgomery  County,   Maryland.      July  17  to  Septeml)er  3,  1869.     75'"'  direction  theodolite 
No.  I.     C.  O.  Boutelle,  observer.     Instrument  16-76  meters  above  ground. 

Hill 

Peach  Grove 

Bull  Run 

Maryland  Heights 

Sugar  Loaf 

Webb 

Soper 

Probable  error  of  a  single  observation  of  a  direction  (D.  and  A'.  ),e,—  ±:  I'^'oS.     Number  of  positions 
of  circle,  VII. 


0 

00 

00  -00 

39 

41 

37  -08 

75 

01 

10-92 

89 

30 

15  -co 

122 

09 

57 '30 

23,3 

17 

59 

•92 

36 

-91 

II 

-16 

0 

00 

00  -QO 

—0  -24 

59  '76 

63 

40 

03  -06 

-0-37 

02  -69 

87 

1 1 

16-57 

+0-04 

16 -61 

131 

27 

54-59 

+0-06 

54  -65 

134 

09 

42-34 

+0-48 

42-82 

297 

19 

37  -68 

+0-01 

37  -69 

342 

13 

41  -17 

0  -00 

41  -17 

CofiHt  (in(L  Geodetic  Survey,   1901.    The  Eastern  ObHtjue.  Arc. 


No.  10 


WfeiA 


Md.ry/and  HeigJits 


Suxfor  Loaf 


Ml  Ma  rah  (til 


Fork 


Kpfit  In  hind    \ 


Marriott 


THE  KENT  ISLAND  BASE 


Triangulatioii  (o  the  Westward  and   Soiithwaid 


Staiiiio  Milfs 


l^nhttrco  h'i>n' 


o  10  2"  .10  'lO  ^0 


Kilometers 

lo  (1  10  ;;o  :<o  »o  ,"io    ""    oo  ro  (>o 


HC   !W«HISKrt 


BASE    LINES    AND    BASK    NETS.  65 


Ahstrads  of  resulting  horizon /a/  directions  observed  and  adjusted  at  stations  forming  the  extension  of 
the  Kent  Island  base  net  to  the  westward  and  southward — coutinuerl. 

Peach  Grove,  Fairfax  County,  Virj^inia.  October  11  to  November  <S,  i<S69,  and  July  2.S  to  Auj^ust  15, 
1870.  75  ""  direction  tlieodolite  No.  i.  CO.  Boutelle,  observer.  Telescope  \y~i2  meters  above 
ground. 

O'^iects  observe..  ^^^^^  "'^^^P'         ^^. 

0  1//  //  // 

Mount  Marshall  o  00  00  "00  — o  •36  59  '64 

Bull  Run  4  36  2966  -j-o'iS  29-84 

Maryland  Heights  58  32  34  06  — o  -50  33  -56 

Sugar  Loaf  79  59  52  76  +0  '06  52  82 

Stabler  143  47  23  '85  +0  -35  24  -20 

Causten  187  26  02  78  ....  

^                                               Hill  194  50  24-85  +0-27  25-12 

Probable  errorof  a  single  observation  of  a  direction  (  D.  and  R.  ),f,=  zt  \"  '02.     Number  of  positions 
of  circle,  VII. 

Sugar  Loaf,  Frederick  County,  Maryland.     August  18  to  November  19,  1879.     50'^"'  di.ection  theodolite 
No.  113.     C.  O.  Boutelle,  F.  D.  Granger,  and  J.  B.  Boutelle,  observers. 

o  /  //  //  // 

Reference  Mark 

Bull  Run 

Mount  Marshall 

Maryland  Heights 

Stabler 

Hill 

Peach  Grove 

Probable  error  of  a  single  ob.servation  of  a  direction  (  D.  and  A*.  ),£>,=  ±  o"  -60.     Number  of  positions 
of  circle,  XI. 

Mount  Marshall,  Rappahannock  County,  Virginia.     July  18  to  September  7,   1S74.     35'^"'  direction 

theodolite  No.  10.     A.  T.  Mosman,  observer. 

a  /  //  //  // 

F'ork 

Maryland  Heights  1S4     15     4956  —0-26 

Sugar  Loaf  202     41     37  50  +0-36 

Bull  Run  225     17     06-78  +0-19 

Peach  Grove  229     31     2999  — o -28 

Clark 

Peters 

Probable  error  of  a  single  observation  of  a  direction  {^D.  and  R.  ),<•,=  d=  i"  -29.     Number  of  positions 
of  circle,  XI. 

4192 — No.   7 — 02 5 


0 

00 

00  -00 

45 

27 

1579 

+  0-72 

I6-5I 

65 

36 

50  -72 

—0  -II 

50-61 

120 

27 

54  '38 

+0  -10 

54  -48 

306 

43 

36-06 

—0  -46 

35-60 

325 

05 

39  25 

352 

26 

27  -18 

—0-26 

26  -92 

0 

00 

00  -00 

1 84 

15 

49-56 

202 

41 

37  -50 

225 

17 

06  -78 

229 

3^ 

29-99 

3" 

50 

33-98 

336 

20 

36-44 

49 

-30 

37 

-86 

06 

-97 

29 

•71 

66 


THE    EASTERN    OBLIQUE    ARC. 


Ahstiacts  of  resulting  horizontal  directions  observed  and  adjusted  at  stations  forming  the  extension  of 
the  Kent  Island  base  net  to  the  ivestxoard  and  south-ward — continued. 

Bull  Run,  Fauquier  County,  Virginia.     September  22  to  November  2S,  1S71.      75' '"  direction  theodolite 

No.  I.     CO.  Boutelle,  observer. 


objects  observed. 


Kcsults  of  local 
adjustment. 


Correction  from  ,,.      , 

fi-ure  adjust-  ^"''\' 

n.eut  seconds. 


Azimuth  Mark 

Clark 

Fork 

Mount  Marshall 

Maryland  Heights 

Sugar  Loaf 

Stabler 

Peach  Grove 


0  00  00  '00 

1  07  09  -35 
33  03  17 -5! 
53  39  05  -53 

157  20  07 -ts 

190  54  06  -98 

225  12  03-95 

242  29  57  -85 


Probable  error  of  a  single  observation  of  a  direction  (  D .  and  A^. ) ,  6'i : 
of  circle,  VII. 


+0-II  05-64 

+0  -49  07  '64 

— o  "68  06  '30 

+0  'oS  04  '03 

o  -00  57  -85 

1^09.     Number  of  positions 


Maryland  Heights.  Washington  County,  Maryland.     September  16  to  October  28,  1870.     75""  direc- 
tion theodolite  No.  i.     CO.  Boutelle,  observer. 


vSugar  Loaf                                                                                         0 

00 

00  -QO 

— Q-lS 

59-82 

Azimuth  Mark                                                                                   0 

57 

03  '66 

Stabler                                                                                                 3 

33 

53  '32 

-0-24 

53  -08 

Peach  Grove                                                                                    30 

31 

14-53 

+0-84 

15-37 

Bull  Run                                                                                            71 

^5 

27  -26 

-0-50 

26-76 

Mount  :Marshall                                                                             106 

43 

12  '67 

-(-0  -08 

'2-75 

Probable  error  of  a  single  observation  of  a  direction  ( D.  and  R. 

),6-x  =  ±0'' 

■93- 

Number  of 

positions 

of  circle,  VII. 

Clark,  Orange  County,  Virginia. 


July  24  to  September  5,  187 1. 
C  O.  Boutelle,  observer. 


75"'"  direction   theodolite  No.    i. 


Spear 

Peters 

Humpback 

Azimut'h  Mark 

P'ork 

Mount  Marshall 

Bull  Run 

Probable  error  of  a  single  observation  of  a  direction  ( D.  and  R. ) ,  t'l  =  ±  i  -03. 
of  circle,  VII. 


0 

00 

00 

-00 

II 

21 

47 

-QO 

24 

09 

37 

■37 

55 

29 

20 

-96 

7« 

26 

10 

-17 

122 

25 

05 

-12 

163 

19 

47 

57 

-I '35 

+0-97 

+0  -02 
+0-4S 
Number  of  positions 


59 

-88 

36 

•02 

II 

■t4 

05 

•14 

48 

05 

basp:  links  and  bask  nets. 


67 


Abslracls  o/rcsullinir  horizontal  dircclions  observed  and  adjusted  at  stations  formiiif;  the  extension  of 
the  Kent  Island  Imse  net  to  the  roestiuard  and  southiuard — continued. 

Fork,  Madison  County,  Virginia.  ()ctot)cr  12  to  December 24,  i<S74.  35""  direction  tlieodolite  No.  10. 
A.  T.  Mosnian,  observer.  July  iS  to  August  6,  1S79.  50""  direction  theodolite  No.  114.  Same 
observer. 


Olijects  ol>serve<l. 


Ke.sult.s  of  local 
adju.stnieiit. 


Correction  from 
figure  adjiisl- 
iiicnl. 


Hinal 
second.s. 


Peaked  o  <x)  tx)  xxi  ....                    

Slate  Springs  20  16  00 '96  -j-o '98  01 '94 

Mount  Marsnall  136  25  13  62  +0  "39  14 'oi 

Bull  Run  f6i  06  37 '64  —I'd  36 '63 

Clark  224  16  5S-6S  — o  "86  57-82 

Peters  270  56  24-5 '  ■■■■                    

Spear  303  52  39-51  — q-io  39-41 

Humpback  322  5S  40-96  —0-20  40-76 

Elliott  Knob  353  33  11-50  4-0-80  1230 

Probable  error  of  a  single  observation  of  a  direction  {D.  and  R. ),  r,  =  it  i'''-24.     Number  of  posi- 
tions of  circle,  XI  in  [874  and  in  1S79. 

Huinpbaefi,  Nelson  County,  Virginia.     June  8  to  29,  1875.  35'^^'"  direction  theodolite  No.  10.     A.  T. 

Mosnian,  observer.      May  11  to  June  6,  1878.  50^'"  direction  theodolite  No.  114.     Same  observer. 

August   18  to  28,    1S79.     50^'"  direction  theodolite  No.  114.  A.  T.  Mo.sman  and  W.  B.  Fairfield, 
observers. 

o  /  /'  //  // 

Jarnian  o  00  00  -cxj  ....                    

Clark  24  30  20-46  -|-i '37  21-83 

Peters  31  40  01  -24  ....                    

Spear  126  14  25  02  +0-44  25-46 

Long  Mountain  154  41  57   10  

Tobacco  Row  173  06  07 -68  — o -87  06 'Si 

Bald  Knob  230  26  24-65  +0-17  24-82 

Elliott  Knol)  265  35  01-13  —''03  00 -lo 

Slate  Springs                                   ^  300  08  53  -99  — o  -57  53  -42 

Fork  357  28  32   18  +0-33  32-51 

Probable  error  of   a    single  observation  of  a  direction  (D.  and    A'.  1,  t',  =  zb  i"-43.  Number   of 
positions  of  circle,  XI. 

Spear,  Buckingham  County,  Virginia.    July  30  to  August  29,  1875.     35^'"  direction  theodolite  No.  10. 
A.  T.  Mosnian,  observer. 

o  /  //  //  t/ 

Willis  o  txi  00  "oo  ....                    

Long  Mountain  113  14  26-50  ....                    

Flat  Top  150  15  15 '49  

Tobacco  Row  160  17  43  42  4-0-22  43  "64 

Humpback  233  59  02  -50  — o  -44  02  -06 

Fork  266  07  14-11  +0-05  14-16 

Peters  283  15  22-59  

Clark  288  05  31-91  -fo-17  32 -aS 

Probable  error  of   a  single  observation  of  a  direction  {D.  and  A'.  ),<■,  =  it  i" -37.  Number  of 
positions  of  circle,  XL 


68 


THE    EASTERN    OBLIQUE    ARC. 


^-Ids/rac/s  of  rcsii/thiff  horizontal  directions  observed  and  adjusted  at  the  stations  forming  the  extension 
of  the  Kent  Island  base  net  to  the  westivard  and  southward — continued. 

Tobacco  Row,  Amherst  County,  Virginia.  September  14  to  23,  1S75.  35'^"'  direction  theodolite  No.  10. 
A.  T.  Mosman,  observer.  September  6  to  9,  1S79.  5o'"'  ilirection  theodolite  No.  114.  Same 
observer. 


Objects  0 

bserved. 

Results  of  local 
adj\istinent. 

0 

f 

If 

Flat  Top 

0 

00 

00  '00 

Bald  Knob 

54 

31 

49  oS 

Humpback 

140 

52 

23-38 

Spear 

200 

'9 

28-80 

Long  Mountain 

272 

56 

37  -39 

Smith 

3if^ 

30 

40-14 

Cahas 

345 

42 

24  -62 

Probable  error  of  a 

.single  observation  of 

a  direction 

(A  an 

\R. 

-)^t\=  -_ 

of  circle  in  1875, 

XL 

Correction  from 
figure  adjust- 
ment. 


Final 
seconds. 


0-65 

48-70 

0-86 

24-24 

0  -21 

2S  -59 

I  ^'-43.    Number  of  positions 


Resulting  angles  and  sides  of  the  Kent  Island  base 


net. 


stations. 

Obsen'ec 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

Taylor 

38 

36 

52-37 

-0-59 

51  -78 

0  -08 

3  -938 

897 

I 

8 

687  -545 

Kent  Island  North  Base 

88 

35 

36-91 

-0  -31 

36-60 

0-08 

4-143 

529 

I 

13 

916-47 

Kent  Island  South  Base 

52 

47 

32  'Ol 

-0-15 

31  -86 

0  -08 

4-044 

816 

9 

II 

0S7  -07 

Marriott 

21 

56 

43-96 

+0-09 

44-05 

0-15 

4-044 

816 

9 

II 

087  -07 

Taylor 

119 

32 

44-32 

+0-17 

44-49 

0-15 

4-411 

765 

6 

25 

808  -67 

Kent  Island  North  Base 

38 

30 

31  -55 

+0-36 

31  -91 

0-15 

4  -266 

498 

4 

18 

471  -34 

Marriott 

40 

ID 

21  -28 

+  0-39 

21  -67 

0  -21 

4-143 

529 

I 

13 

916-47 

Taylor 

80 

55 

51   -95 

+  0-76 

52-71 

0  -22 

4  -328 

444 

0 

21 

303-16 

Kent  Island  vSouth  Base 

58 

53 

46-24 

+0-03 

46-27 

0  -22 

4  -266 

498 

5 

18 

471  -34 

Marriott 

18 

13 

37-32 

+0-29 

37 -6j 

0-14 

3  -938  897 

I 

8 

687  -545 

Kent  Island  North  Base 

50 

05 

05-36 

-0-66 

04-70 

0-15 

4  -328 

444 

I 

21 

303-16 

Kent  Island  South  Base 

III 

41 

18  -25 

—0  -12 

18-13 

0-15 

4-411 

765 

8 

25 

808  -68 

Linstid 

34 

46 

24-83 

+  1  -QI 

25 -84 

0  -09 

4-044 

S16 

9 

I  I 

087  -07 

Kent  Island  North  Base 

32 

26 

27-42 

+0-28 

27-70 

0-09 

4  -018 

198 

2 

10 

427  -93 

Taylor 

112 

47 

05-71 

-)-I   -02 

06-73 

0  -09 

4-253 

398 

I 

17 

922  -48 

Linstid 

33 

57 

08  -85 

-I   -25 

07  -60 

0-13 

4  -266 

498 

5 

18 

471  -34 

Taylor 

127 

40 

09  -97 

-I  -18 

08-79 

0-13 

4-417 

956 

2 

26 

179-19 

Marriott 

18 

22 

44-54 

-0-54 

44-00 

0-13 

4  -018 

198 

2 

10 

427  -93 

Linstid 

68 

43 

33  -68 

— 0-24 

33-44 

0-37 

4-411 

765 

7 

25 

808  -67 

Kent  Island  North  Base 

70 

56 

58  '97 

+0-64 

59-61 

0-37 

4-417 

956 

2 

26 

179-19 

Marriott 

40 

19 

28  -50 

-0-44 

28  -06 

0-37 

4-253 

398 

2 

17 

922  -48 

I 


BASE   LINES    AND    BASE   NETS. 


69 


Resulliiiff  aiif^lcs  and  sides  of  the  Kcnl  Island  base  iie/ — continued. 


I 


13 


14 


15 


i6 


iS 


19 


Stations. 

Observet 

angles. 

Correc- 
tion. 

S])her- 

ical 
angles. 

Spher- 
ical 
exce.ss. 

Log.  dis- 
tances. 

Distances  in 
meters. 

0 

f 

// 

// 

// 

// 

Webb 

76 

16 

06 '19 

+0-27 

06  -46 

0  -33 

4-4'7 

956 

2 

26 

179-19 

Linstid 

66 

18 

42-31 

-1-0 -52 

42  -83 

0  -33 

4-392 

324 

7 

24 

678  -84 

Marriott 

37 

25 

II  -13 

+0-58 

II  -71 

0  -34 

4-214 

204 

0 

16 

375  -^6 

Fiiilay 

25 

43 

36-20 

+0-97 

37  ■  1 7 

0-49 

4-214 

204 

0 

16 

375  --^6 

Linstid 

84 

01 

06  -4  r 

-ho -69 

07  'lO 

0-49 

4-574 

261 

9 

37 

5'9'92 

Webb 

70 

15 

16-99 

-|-0  -21 

17  •20 

0-49 

4-550  316 

3 

35 

507-19 

Pooles  Island 

79 

44 

39-79 

—  0  -64 

39-15 

0  -64 

4-550 

3'6 

3 

35 

507-19 

Linstid 

46 

42 

57-73 

-0-89 

56  -84 

0-63 

4-419 

418 

8 

26 

267  -50 

Fin  lay 

53 

32 

27  -II 

-1-20 

25-91 

0-63 

4-462 

7.6 

4 

29 

021  -27 

Swan  Point 

56 

08 

57  92 

+0-74 

58  -66 

0-25 

4-253 

39« 

2 

17 

922  -48 

Kent  Island  North  Base 

60 

07 

41  -14 

+0-07 

41   -21 

0-25 

4-272 

151 

1 

18 

7f3-33 

Linstid 

63 

43 

20  -63 

-fo-26 

20  -89 

0  -26 

4-286 

6S9 

I 

19  350  -36 

Swan  Point 

"3 

07 

27-59 

—  0  -81 

26  -78 

0-23 

4-462 

716 

4 

29 

021  -27 

Linstid 

30 

30 

19-24 

-0-33 

iS  -91 

0-23 

4-204 

626 

-* 

16 

oiS  -66 

Pooles  Island 

36 

22 

15  -13 

—  0  -12 

15-01 

0  -24 

4-272 

'51 

2 

18 

713  -34 

Osbornes  Ruin 

77 

29 

15  -76 

—0  -04 

15-72 

0  -37 

4-419 

418 

8 

26 

267  50 

Pooles  Island 

54 

27 

12-11 

—  I   -20 

10  -91 

0  -36 

4-340 

2S9 

4 

21 

892  -20 

P'inla}' 

48 

"3 

34  -63 

-0-17 

34  -46 

0  -36 

4  -301 

337 

t) 

20 

014-14 

Turkey  Point 

44 

01 

48-72 

—  I  -09 

47  -63 

0-39 

4-301 

337 

0 

20 

014-14 

Pooles  Island 

54 

30 

55-00 

-}-I  -19 

56-19 

0  '39 

4-370 

lOI 

8 

23 

447-78 

Osbornes  Ruin 

81 

27 

17-53 

-0-17 

17-36 

0  -40 

4-454 

483 

8 

28 

476  -32 

Weste 

11  an 

(/  souther)!  e.\ 

■tension  of  Kent  Island  has 

('  net. 

Hill 

56 

40 

32-00 

-|-o-o8 

32-08 

0-46 

4-392 

324 

7 

24 

67S  -84 

Webb 

53 

ID 

52-09 

0  -oo 

52-09 

0  -46 

4  -373 

719 

9 

23 

643  94 

Marriott 

70 

o>S 

36-93 

+0-29 

37-22 

0-47 

4  -443 

721 

' 

27 

779  29 

Soper 

39 

41 

37  -08 

-  -  0  -09 

36-99 

049 

4  392 

324 

7 

24 

678  -84 

Webb 

102 

15 

58-28 

0  -00 

58  -28 

0  -48 

4  -577 

012 

I 

37 

75S  -27 

Marriott 

3^ 

02 

26-57 

-0-38 

26-19 

0-49 

4  376 

775 

6 

23 

810-89 

Soper 

75 

01 

10  -92 

+0-32 

II  -24 

0  -43 

4  -443 

721 

I 

27 

779  -29 

Webb 

49 

05 

06-19 

0  -ot) 

06  - 1 9 

0  -42 

4  -337 

076 

1 

21 

730  -82 

Hill 

55 

53 

43-41 

+0  -43 

43  •S4 

0-42 

4  -376 

775 

S 

23 

810  -90 

Soper 

35 

19 

33  -84 

-t-0-41 

34-25 

0  -40 

4  -373 

719 

9 

23 

643  "94 

Marriott 

32 

06 

10-36 

+0-67 

II  -03 

0  40 

4  -337 

076 

2 

21 

730  -82 

Hill 

112 

34 

15  -41 

f  0  -5 1 

15  92 

0  -40 

4  -577 

012 

2 

37 

758  -28 

Stabler 

44 

54 

03-49 

-o-or 

03  -48 

0  -oS 

4  -376 

775 

7 

25 

810-90 

Webb 

8 

23 

06-84 

— 0  -02 

06-82 

o"oS 

3  -691 

882 

4 

4  919  06 

Soper 

126 

42 

49-94 

0  -oS 

4-432 

017 

4 

27 

040  -67 

JO 


THE    EASTERN    OBLIQUE    ARC. 


No. 


23 


24 


25 


26 


27 


2S 


29 


30 


31 


32 


IVcUvu 

and  southern 

extension  uf  Kent  Island  t>ase  net- 

-continued. 

stations. 

Observed 

angles. 

Correc- 
tion. 

.Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

rr 

// 

// 

// 

Stabler 

62 

40 

22-32 

~o  -26 

22  -06 

0-53 

4  -443 

721 

I 

27 

779  -29 

Webb 

57 

28 

13  '03 

—0  -02 

13-01 

0-54 

4-420 

998 

3 

26 

363  -21 

Hill 

59 

51 

26-62 

-0-08 

26  -54 

0-54 

4  -432 

017 

4 

27 

040-67 

Stabler 

17 

46 

18  -83 

-0  -245 

18  -585 

0  -034 

4  -337 

076 

1 

21 

730  -82 

Soper 

15S 

15 

58  -820 

0-033 

4-420 

998 

3 

26 

363  -21 

Hill 

3 

57 

43  '21 

-0-514 

42  -696 

0  -034 

3  -691 

882 

5 

4 

919  -06 

Peach  Grove 

51 

03 

01  'OO 

—0-08 

00  -92 

0  '62 

4  -420  998 

3 

26 

363-21 

Stabler 

63 

40 

03  -06 

-0-13 

02-93 

0  -62 

4-482 

609 

8 

30 

381  -54 

Hill 

65 

16 

57  '50 

+0-50 

58-00 

0  -61 

4  -488  456 

8 

30 

793  -34 

Sugar  Loaf 

18 

22 

03-65 

0  -62 

4  -420  99S 

3 

26 

363-21 

Stabler 

134 

09 

42  '34 

+  0-73 

43-07 

0  -61 

4-778 

281 

4 

60 

017  -99 

Hill 

27 

28 

15-03 

+0  -10 

15-13 

0  -62 

4-586 

513 

6 

38 

593  '45 

vSugar  Loaf 

45 

42 

51  -12 

+  0  -20 

51  -32 

0-95 

4  -488  456 

8 

30 

793  '34 

Stabler 

70 

29 

39  -28 

+  0-85 

40-13 

0  -94 

4-607 

957 

7 

40 

546-91 

Peach  Grove 

63 

47 

31  -09 

+0-30 

31  -39 

0  -95 

4  -586 

513 

6 

38 

593  -45 

Sugar  Loaf 

27 

20 

47-66 

0  -95 

4  -482 

609 

8 

30 

381  -54 

Hill 

37 

48 

42  '47 

^-o  -40 

42-87 

0-95 

4-607 

957 

8 

40 

546  -92 

Peach  Grove 

114 

50 

32  -09 

-)-o  -22 

32-31 

0-94 

4-778 

281 

4 

60 

017-99 

Maryland  Heights 

3 

33 

53-32 

-0  -059 

53  -261 

0  -104 

4-586 

513 

6 

38 

593  -45 

Sugar  Loaf 

173 

44 

18  -32 

+0  -562 

18  -882 

0  -104 

4-830 

573 

0 

67 

697  -56 

Stabler 

2 

41 

47-75 

+0-419 

48  -169 

0  -104 

4-465 

432 

7 

29 

203  -35 

Marylanil  Heights 

30 

31 

14-53 

+1  -02 

15  -55 

0-79 

4-607 

957 

7 

40 

546  -91 

Sugar  Loaf 

128 

01 

27  -20 

+0-36 

27  -56 

0-79 

4  -798 

611 

0 

62 

894  -26 

Peach  Grove 

21 

27 

18  -70 

+0  -.56 

19  -26 

0-79 

4-465 

432 

7 

29 

203  -35 

Maryland  Heights 

26 

57 

21   -21 

+ 1  -08 

22  -29 

1-63 

4  -488  456 

8 

30 

793  -34 

Stabler 

67 

47 

51   -53 

+0-43 

51  -96 

'-63 

4-798 

611 

I 

62 

S94  -28 

Peach  Grove 

85 

14 

49  79 

+0-86 

50-65 

I  -64 

4-830 

573 

0 

67  697  -56 

Bull  Run 

33 

33 

59  -83 

-1  -16 

58-67 

I  -20 

4-465 

432 

7 

29 

203  -35 

Maryland  Heights 

71 

25 

27  -26 

-0-31 

26-95 

I  -20 

4-699 

551 

7 

50 

067  -01 

Sugar  Loaf 

75 

00 

38  -59 

—0-62 

37  -97 

I  -19 

4  707 

753 

2 

51 

021  -49 

Bull  Run 

67 

51, 

56-80 

—0  -40 

56-40 

2  -70 

4-830 

573 

0 

67  697  -56 

Maryland  Heights 

67 

51 

33-94 

—0  -26 

33-68 

2-71 

4-830 

553 

5 

67  694  -52 

vStabler 

44 

16 

38  -02 

f  0  -02 

38-04 

2-71 

4-707 

753 

2 

51 

021  -49 

Hull  Run 

85 

09 

50  -70 

—0-49 

50  -21 

1  -77 

4  -798 

611 

0 

62 

894  -26 

Maryland  Heights 

40 

54 

12-73 

-I  -33 

11  -40 

.-78 

4  -616 

253 

0 

41 

328  -82 

Peach  Grove 

53 

56 

04-40 

-0  -68 

03-72 

1-78 

4-707 

753 

3 

51 

021-51 

Bull  Run 

34 

17 

56-97 

+0-76 

57  '73 

I  -62 

4-586 

513 

6 

38 

593  -45 

Sugar  Loaf 

98 

43 

39-73 

+  1  -iS 

40-91 

I  -61 

4-830 

553 

5 

67  694  -52 

Stabler 

46 

58 

25-77 

+Q-44 

26-21 

1  -62 

4-699 

55' 

6 

50 

067  -00 

BASE    LINES    AND    BASE    NETS. 


71 


33 


34 


35 


36 


37 


3« 


39 


40 


41 


42 


43 


44 


45 


IVcshTll 

and  son/Zicrii 

c.vlfi/sutii  of  Kcnl  Island  base  net — 

-continued. 

Stations. 

( )bservc(l 

aiij^les. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 

excess. 

I,og.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

Hull  Run 

51 

35 

50-87 

4-0-68 

51  -55 

1  -37 

4  (*'>1 

957 

7 

4" 

.546  -91 

Sugar  Loaf 

53 

00 

48  -61 

io-98 

49  "59 

'-37 

4-616 

253 

0 

41 

328  -82 

Peach  Grove 

75 

23 

23  'lo 

^a-i2 

22-98 

■-38 

4-699 

551 

7 

50 

067  01 

Bull  Run 

'7 

>7 

53  '90 

0  -08 

53  •«2 

f)  -70 

4  -488  456 

8 

30 

793  -34 

vStabler 

23 

31 

13-51 

+0-41 

13-92 

0  -70 

4  -616 

253 

I 

4J 

328  -83 

Peach  Grove 

139 

10 

54   '9 

1  o-i8 

54  -37 

0-71 

4  -830 

553 

6 

67 

694  -53 

Mount  Marshall 

iS 

25 

47-94 

+0-62 

4S  -56 

,79 

4-465 

432 

7 

29 

203  35 

Maryland  Heights 

106 

43 

12  -67 

+  0-26 

12-93 

1-78 

4-946 

793 

1 

88 

469  -4 1 

Sugar  Loaf 

54 

51 

03-66 

-|-0  -21 

03  -87 

I  '79 

4-878 

122 

3 

75 

530  -49 

Mount  Marshall 

41 

01 

17  -22 

+  "  -45 

17  -67 

I  -88 

4-707 

753 

2 

51 

021   49 

Maryland  Heights 

35 

17 

45  -41 

+  0-57 

45  •9-'^ 

I  -88 

4  652 

400 

4 

44 

915-93 

Bull  Run 

i«3 

41 

01  -62 

+0  •3<S 

02  -00 

I  89 

4  -878 

122 

2 

75 

530  -47 

Mount  Marshall 

45 

15 

40-43 

—0  -01 

40-42 

3  90 

4  -798 

611 

0 

62 

S94  -20 

Maryland  Heights 

76 

II 

5S-14 

—0-76 

57  •3« 

3-91 

4  -934 

439 

0 

85 

988  -24 

Peach  Grove 

58 

32 

34-06 

-0-15 

33-91 

3-90 

4  -878 

122 

3 

75 

530  49 

Mount  Marshall 

22 

35 

29  28 

-0-17 

29-11 

I  -29 

4-699 

551 

7 

50 

067  01 

Sugar  Loaf 

20 

09 

34  -93 

—0-83 

34-10 

I    29 

4-652 

400 

5 

44 

915  94 

Hull  Run 

137 

15 

01  -45 

^0  -78 

00  -67 

I  -30 

4-946 

793 

I 

88 

469  -41 

Mount  Marshall 

26 

49 

52-49 

-0  -63 

51  -86 

2-91 

4-607 

957 

7 

40 

546  •91 

Sugar  Loaf 

73 

10 

23-54 

^0-15 

23-69 

2-91 

4-934 

439 

I 

85 

988  -25 

Peach  Grove 

79 

59 

52  -76 

+0-41 

53-17 

2  90 

4-946 

793 

> 

88 

469  41 

Mount  Marshall 

4 

14 

23-21 

-  0  -46S 

22  -742 

0  -242 

4  616 

253 

0 

41 

328  -82 

Bull  Run 

171 

09 

07-68 

(  0  -III 

07  -791 

0  -241 

4  -934 

439 

0 

85  988-24 

Peach  Grove 

4 

36 

29  -66 

■\  0  -532 

30-192 

0  -242 

4-652 

400 

4 

44 

9>5  93 

Clark 

40 

54 

42  -45 

+0-46 

42-91 

2  -07 

4  652 

4fxi 

4 

44 

9 '5  93 

Mount  Marshall 

86 

33 

27  -01 

0  -25 

26  76 

2  06 

4-S35 

447 

I 

68 

461   61 

Bull  Run 

52 

3' 

56-29 

"t-o  -24 

56  -53 

2  -07 

4  -735 

883 

3 

54 

435  -63 

Fork 

24 

4" 

24  -02 

~i-lo 

22  62 

I  -02 

4-652 

400 

4 

44 

915  93 

Mount  Marshall 

134 

42 

53  -03 

—0  19 

52-84 

I  -03 

4-883 

177 

2 

76 

414-75 

Hull  Run 

20 

35 

4S-13 

-0  -52 

47-61 

I  02 

4  -577 

810 

2 

37 

827  -72 

Fork 

S7 

51 

45  -06 

~I  -25 

43  -81 

I  -29 

4-735 

883 

3 

54 

435  -63 

Mount  Marshall  , 

4.S 

(19 

26-02 

+0-05 

26  07 

1  -30 

4  -608 

327 

0 

40 

58 1  40 

Clark 

43 

S'"^ 

54  95 

0-94 

54  -01 

'  -30 

4  '577 

8 10 

3 

37 

827  -73 

I-'ork 

63 

U) 

2 1   04 

:  0-15 

21  -19 

2  34 

4  -835 

447 

1 

68 

461  61 

Bull  Run 

3' 

56 

08-16 

1  076 

08  -92 

2-34 

4-608 

326 

9 

40 

581  -39 

Clark 

S4 

53 

37  -40 

-0  -48 

36  -92 

2  '35 

4-883 

177 

2 

76 

414-75 

Humpback 

27 

01 

48  -28 

t  I  -04 

49  -32 

2  46 

4-608 

326 

9 

40 

581  -39 

I'ork 

qS 

41 

42  -28 

-\  0  -67 

42  -95 

2  47 

4-945 

819 

I 

SS 

271  -22 

Clark 

54 

16 

32  -80 

i  2  -32 

35-12 

2  46 

4  -860 

307 

4 

72 

404  -8q 

72 


THE    EASTERN   OBLIQUE    ARC. 


IVt'stei-i! 


No. 


46 


47 


48 


49 


Spear 

Humpback 

Fork 

Spear 

Humpback 

Clark 

Spear 

Fork 

Clark 

Tobacco  Row 

Humpback 

Spear 


son/ 

//(V7/ 

twiensioi!  of  Kent 

Island 

ha  St 

)iet~ 

-contiuued. 

Observed  angles. 

Correc- 
tion. 

.Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  dis. 
tances. 

Distances  in 

meters. 

0 

/ 

// 

// 

// 

// 

32 

oS 

II  -61 

+0-49 

12-10 

2 

'3 

4  -S60 

307 

4 

72   494-89 

128 

45 

52-84 

+0  -I  I 

52-95 

2 

-14 

5-026 

395 

5 

106    266  -29 

19 

06 

01  '45 

—0  -lo 

oi  -35 

2 

•13 

4-649 

283 

4 

44  594-7' 

54 

06 

29-41 

+0  -61 

30-02 

3 

•26 

4-945 

819 

1 

88   271  -22 

lOI 

44 

04-56 

-0  -93 

03  -63 

3 

■27 

5  -028 

099 

9 

106  6S4  -15 

24 

09 

37  '37 

-I  -23 

36-14 

3 

-26 

4-649 

283 

4 

44  594-71 

21 

58 

17  -80 

+0-12 

17-92 

3 

•59 

4  -608 

326 

9 

40  581  -39 

79 

35 

40-83 

+0-77 

41  -60 

3 

■59 

5  -028 

100 

0 

106  684  -17 

78 

26 

10-17 

+ 1  -08 

II  -25 

3 

•59 

5-026 

395 

5 

106  266  -29 

59 

27 

05  -42 

—  I  '08 

04  '34 

I 

■37 

4-649  283 

4 

44  594-71 

46 

51 

42-66 

-I  '3' 

41  '35 

I 

•37 

4-577 

326 

2 

37  785  -59 

73 

41 

19  -qS 

— 0-66 

18-42 

I 

■37 

4-696 

339 

5 

49  69S  -07 

Determination  of  the  probable  error  of  the  lengtli  of  the  sides  Osbomes  Rjiin  to  Turl<:ev  Point, 

and  Tobaeeo  Row  to  Spear. 

In  connection  with  the  Kent  Island  base  net  the  probable  error  of  the  side  Linstid 
to  Finlay  was  rigorouslj-  computed,  and  was  found  to  be  ±0-33  meters;  which  equals 
ToT^fiTTu  part  of  the  length  of  the  side.  There  are  three  triangles  between  this  side  and 
the  side  O.sbornes  Ruin  to  Turkey  Point;  but,  instead  of  computing  the  additional  prob- 
able error  arising  from  their  measure  separately,  it  will  suffice,  when  estimating  the 
probable  error  of  the  chain  of  triangles  between  the  Fire  Island  and  Kent  Lsland  bases 
to  include  the.se  three  triangles  as  part  of  the  chain;  otherwise,  the  probable  error  of  the 
line  ma\-  be  taken  as  about  yoo^-oirTr  part  of  the  length. 

For  the  extension  southward  the  probable  error  of  the  side  Webb  to  Marriott  was 
rigorously  computed  and  found  to  equal  ±0-22  meters,  which  is  about  tt2'-2tto  part  of 
the  length.  For  that  part  of  the  triangulation  lying  between  Webb  to  Marriott  and 
Fork  to  Clark  the  probable  error  was  found  to  be  foa'Triyiv  part  of  the  length,  and  the 
.same  fraction  may  be  used  for  the  extension  thence  to  the  line  Tobacco  Row  to  vSpear. 

Descriptions  of  the  base-net  station.s-  are  given  in  the  account  of  the  Transconti- 
nental Triangulation,  etc..  Special  Publication  No.  4,  Washington,   1900. 

5.    THE    ATLANTA    BASE    AND    BA.SE    NET,   GEORGIA,    1872-73. 
Location,  measurement,  and  resnltini;  lenoth  of  the  Atlanta  base  line,  i8'j2-'j^. 

The  Atlanta  ba.se  is  located  on  Peach  Tree  Ridge,  Georgia,  about  24  kilometers 
(or  15  .statute  miles)  northeast  of  the  city  of  Atlanta.  It  is  the  .seventh  and  last  base 
measured  with  the  Bache-Wiirdeniann  apparatus,  and  is  the  only  one  measured  with  it 
more  than  once.  It  is  9)^  kilometers  (or  5-81  statute  miles)  in  length  and  was  meas- 
ured three  times.  There  is  a  very  full  description  of  the  operations  in  Coast  Survey 
Report  for  1873,  Appendix  No.  12,  pages  123-131,  and  the  description  of  the  apparatus 


BASE    LINES   AND    BASE   NETS.  73 

is  given  in  Coast  Survey  Report  f(;r  1854,  Appendix  No.  35,  and  in  Coast  Survey  Report 
for  1873,  Appendix  No.  12.  F^urther  remarks  will  be  found  in  the  account  of  the 
Dauphin  Island  and  the  Hpping  bases  in  this  publication.  It  will  also  appear  from 
the  seven  values  collected  on  page  131  of  the  Rejjcjrt  tor  [873  that  the  average  accuracy 
reached  with  this  apparatus  is  about  goo'ouu  P^rt  of  the  length  measured.  In  \-iew  of 
the  complete  publication  already  made,  it  will  .suflfice  to  give  the  present  account  in  an 
abbreviated  form. 

The  middle  point  of  the.base  is  in  latitude  33°  54'"4  and  longitude  84°  i6'-5,  with  a 
mean  azimuth  52°  o8''2.  The  measurements  were  made  by  Assistant  C.  O.  Boutelle. 
The  first  and  second  measures  were  made  in  opposite  directions  in  Novemljer  and 
December,  1872,  and  in  January,  1873,  and  the  third  was  made  in  July  and  August, 
1873.  The  three  measures  were  accomplished  in  17,  13,  and  14  working  days,  re.spec- 
tively.  In  connection  with  these  several  measures  the  tubes*  were  frequenth'  compared 
for  length  with  the  standard  bar,  which  was  immersed  in  glycerin  during  the  July  and 
September  comparisons. 

The  summit  of  the  ridge  is  narrow  and  crooked,  Imt  the  slope  of  the  measurement 
was  confined  within  the  maximum  inclination  the  tubes  would  bear,  namely,  5°.  A 
gulch  near  the  southwest  end  was  crossed  on  trestlework  consisting  of  two  separate 
structures.  The  approximate  elevation  above  sea  level  is  320  meters.  The  terminals 
are  marked  by  granite  monuments  and  the  subdi\-isionsof  the  line  by  small  granite  posts. 

The  length  of  the  6-meter  standard  bar  is  5'" '999  941  at  0°  C.,and  its  coefficient  of 

dz   2 

expansion  o '000  01 1  54.      The  luimerous  comparisons  made  for  standardization  of  the 

±4 
tubes  and  for  testing  their  compen.sation  showed  that  the  latter  was  .still  clo.se:  that  is. 
about  2 1  parts  of  22  remained  compensated  between  the  range  of  temperature  0°  to  22°  C. , 
but  between  the  temperatures  from  22°  to  38°  C.  the  tubes  compen.sated  only  aliout  10 
parts  in  11.  The  comparisons  were  made  with  the  Saxton  reflecting  comparator  Xo.  i . 
for  which  we  have  for  the  period  November,  1872,  to  January,  1873,  one  division  at 
4>2°  C.  equal  i'384  microns  and  at  19°  C.   r378  microns,  values  answering  for  the  case 

±3  ±3 

of  the  first  and  .second  base  mea.sures  In  connection  with  the  third  measure,  ob.serva- 
tions  in  July  and  September,  1873,  gave  r  div.  =  i'376  /'.  We  have  also  i  turn  of  the 
screw  at  the  temperatures  4°,  19°,  and  28°  C.  equal  to  35o'9,  352"3.  ^uid  353'o6  scale 

±  -18 

divisions,  respectively. 

As  the  result  from  the  above  comparisons  we  have  the  following  values  for  the  length 
of  the  tubes,  in  which  the  uncertainty  from  the  length  of  the  standard  is  included: 


For  first  and  second  nieasnres 


and  fcr  third  measure 


Tube  I,  =  5'" '999  999  7  +  o'ooc^  003  37  (  /  -  1 1^-2  C. ) 

'  =b  144 

Tube  2=5    -999  647  8    ;   Q-txx)  004  84  (/  —  U^'2  C. ) 

±193 

Tube  I ,  =  6""ooo  0S4  6  4-  o-ooo  009  54  (/  —  27''-6  C.  ) 

±112 

Tube  2=5    999  730  3   t  0XXX1  cxjS  01  (/  —  27°  "S  C. ) 
±116 


♦Before   making   the   compari.sons  tube   No.  i  was  supplied  with   a  new  agate.     The  Borda  .-teate  or  differential 
thermometer  as  applied  to  the  tubes  is  shown  on  plate  No.  iS  in  the  Coast  Sur\-ey  Report  for  1S7,;. 


74 


THE    EASTERN    OBLIQUE    ARC. 


The  minimum  temperature  at  which  the  tubes  were  used  was  —  7°  7  C,  and  many 
were  laid  with  temperatures  below  the  freezing  point;  the  maximum  temperature  at 
which  the  tubes  were  used  was  41 '^'7  C,  and  many  were  laid  with  temperatures  above 
38°  C.  The  three  thermometers  attached  to  each  tube  were  read  and  the  mean  values 
were  corrected  for  graduation  errors.  The  maximum  inclination  of  a  tube  laid  was  4° '7, 
and  there  were  a  great  many  with  inclinations  of  4°.  The  ruggedness  of  the  ground 
caused  the  sum  of  the  inclination  corrections  for  the  whole  base  to  mount  up  to  io""22i2 
in  the  first  and  to  10'" '0375  in  the  last  measure.  Fractional  parts  of  a  tube  at  the  base 
monuments  and  intermediate  marks  were  measured  with  the  brass  Lenoir  meter  of  the 
vSurvey,  which  is  of  standard  length  at  13° '6  C. 

The  following  table  shows  the  temperature  of  the  tubes  during  the  measures  of  the 
several  parts  of  the  base,  their  lengths  as  measured,  corrected  for  inclination,  but  not 
reduced  to  sea  level,  and  exhibits  the  difference  of  the  individual  measures  from  the 
mean  of  the  three  measures: 


Subdivisions 
of  base. 

Temperatures, 

Resulting  length. 

Mean. 

Discrepancies. 

First 
measure. 

Second 
mea.sure. 

Third 
measure. 

First           Second, 
measure.      measure. 

Third 
measure. 

First 
measure. 

Second 
measure. 

Third 
measure. 

SW  to  I 
I  to  n 
U  to  M 
.M  to  IV 

IV  to  V 

V  to  NE 

c. 

i5'i3 
5-10 
6-84 

II  "06 

14-0? 
11  31 

C. 

5-62 
9  "44 

4  -28 
2-97 

5  "57 
12  92 

C. 

34-33 
.       33 "94 
32 '56 
32  03 
31-96 
30  "74 

I  635 "974  9 
I  642-313  6 
I  234 -383  3 
I  348  -886  2 
I  785  -709  0 
I  691 -692  0 

I  635 -96S  0 
I  642-3173 
I  234 -388  0 
I  348  -880  6 
1  785  -704  8 
I  691  -692  5 

I  635  -966  4 
I  642-3125 

I  234-391  8 
1  348  -8S5  I 

I  785  -705  2 
I  691  -681  5 

I  635  -969  8 
1  642  -314  4 
I  234 -387  7 
I  348  -884  0 
I  785 -706  3 
I  691  -688  7 

Ill  III . 

-5-1 

+0-8 
+4-4 
—  2-2 
-2-7 
-3-3 

mm. 

+  1-8 
-2-9 
-0-3 
+3-4 
+  1-5 
-3-8 

mm. 

+3-4 
+  1-9 
-4-1 
-I  -J 
+  1  -I 
4-7-2 

Whole  base 

10-58 

6 -.So 

32-59 

9  338 -959  0 

9338-951  2 

9  338  -942  .'s 

9  338  -950  9 

The  frequent  changes  of  sign  in  the  above  discrepancies  may  be  taken  as  a  favor- 
able indication  that  the  lengths  of  the  tubes  were  correctly  determined.  In  order  to 
o]:)tain  the  data  required  to  reduce  each  part  of  the  base  to  sea  level,  two  lines  of  spirit 
levels  were  carried  over  it,  double  zenith  distances  of  Stone  Mountain  were  measured 
for  difference  of  height  at  Southwest  Base,  Middle  Base,  and  Northeast  Base,  and 
reciprocal  ob.servations  were  made  at  Stone  Mountain.  A  line  of  spirit  levels  was 
carried  from  Stone  Mountain,  in  1873-74,  to  Augusta,  Georgia;  between  this  place  and 
Port  Royal  the  railroad  levels  were  utilized,  and  the  elevations  refer  to  Atlantic  half 
tide  at  Beaufort,  vSouth  Carolina.  The  resulting  height  of  vStone  Mountain  is  5 13'" '95, 
and  allowing  i""52  for  the  elevation  of  tlie  tubes  above  the  ground,  the  average  eleva- 
tion of  the  tubes  above  the  half-tide  level  becomes  321'" '5,  and  the  reduction  of  the  base 

Whence  we  get  for  the  length  of  the  ba.se  the  values 


to  sea  level  —       = 


P 


o    4710. 
9  338" 


-4880 

4802  \  mean  9  338  479  9  meters. 

47 '  5  I 

Combining  the  mcmi  of  the  two  winter  measures  with  the  value  of  the  summer 
measure,  we  get  9  338 "477  8  meters.  We  have  also  the  distance  Southwest  Ba.se  to 
Middle  Base  4  5i2'"-447,  and  from  Middle  Ba.se  to  Northwest  Ba.se  4  826-032  meters. 
The  liorizontal   angles  mea.sured  at  these  three  ba.se  stations  and  at  Stone  Mountain 


BAS?:    LINES    AND    HASE    NETS.  75 

afford  a  check  on  the  measure.      vStartin^  with  the  first  or  sh(;rter  distance  and  usinj^ 
the  adjusted  anj^ular  measures,  the  length  of  tlie  base  thus  trigtjnometrically  deduced 

comes  out  9  338"''502,  or  22 '  in  excess  of  the  direct  hnear  measure. 

For  the  ])robable  error  of  the  measure  of  the  l)a.se  we  have  the  following  data: 
Probable  error  from  uncertainty  in  length  of  tubes  in  i  556  tubes,  i  556  X  i^oj-i^ 
±o"''02i  78.  For  mere  measuring  error  we  have,  after  forming  the  values  ^  S-,  2:  6  '-, 
2  (J^^,  etc.,  where  the  f^'s  are  taken  from  the  preceding  tal)le  of  differences  from  the 
mean  of  three  measures,  assumed  of  equal  weight,  the  probable  error  of  the  ba.se  from 

the.se  measures  =  zh  o'674  (        -  '  =  ^  )^"    where  Ji  —  i,,    hence   tlie 

V  n(n-i}  J 

result  =  dco"''oo3  85,  which  includes  errors  ari.sing  from  defective  compensation,  errors 

of  contact,  of  tran.sfer  to  ground  or  to  monuments,  of  alignment  and  inclination,  etc. 

Supposing  an  uncertainty  in  //  of  i  meter,  the  reduction  to  sea  level  changes 
±  i"'"'-46. 

Combining  the  values  we  get  the  probable  error  of  the  ba.se 

V(2r78)="+~(y85)^+  (1-46)=  =  db  22--2, 

which  equals  jji'iumi  P^rt  of  the  length. 

The  resulting  length  of  the  ba.se  is  9  338'477  8  meters,  and  its  logarithm  3^970  276  09 

±222  ±  I  03 

Adjiistiiieiil  of  tht'  .Allan la  base  net. 

The  base  is  connected  with  the  principal  triangulation  by  a  rather  complex  system 
of  triangles,  which  made  the  placing  of  the  boundary  of  the  net  to  some  extent  an 
arbitrary  act,  except  in  so  far  as  the  labor  involved  set  a  limit  to  it.  The  net  as  it  had 
been  selected  and  adjusted  in  1876  is  here  retained  as  sati.sfactory.  The  only  change 
that  could  be  made  would  be  the  introduction  of  the  small  corrections  to  the  horizontal 
directions  for  height  of  object  observed  upon,  which  it  was  not  customary  to  introduce 
at  that  time. 

The  heights  of  the  10  stations  involved  are  as  follows: 

Appyoxiiitatc  hcti^hls  of  slalioiis  alwzY  llw  Atlantic  Ocean. 

Mettrs.  I'ect. 

Atlanta  Southwest  Base 

Atlanta  Northeast  Base 

Atlanta  Middle  Base 

Stone  ^Mountain* 

Academy 

Kenesaw 

Sweat  Mountain 

Sawnee 

Pine  Log 

Grassy 


3 1  •^•5 

■  045 

326 

1  070 

325 

1  06S 

514 

1  6S6 

346 

1  136 

55" 

1  S09 

516 

1  694 

600 

I  967 

7 '3 

2  340 

I  003 

3  290 

*  Klevatio!!  from  spirit  level.s.  .si.V'o?. 


76 


THE    EASTERN    OBLIQUE    ARC. 


No.  12. 


This  reduction  of  the  directions  to  sea  level,  a  maximum  in  the  case  of  line  Pine 
Log  to  Grassy,  is  less  than  o"'o-j,  and  in  general  it  is  less  than  one-half  of  this  amount. 
It  is  therefore  fully  covered  by  the  observing  error  of  the  directions  which  on  the  aver- 
age amounts  to    "^  ^  or  o"'i9;  besides,  a  number  of  directions  require  corrections  in  the 

77 
figure  adjustment  of  more  than   i". 

As  shown  in  the  diagram,  the  net  comprises  Testations  which  were  occupied  between 
1872  and  1874;   two  observers  were  engaged  in  the  work  and  three  different  instruments 

were  employed,  one  being  a 
repeating  theodolite.  The  ad- 
justment of  the  observations 
of  directions  at  a  .station  was 
made  by  Bessel's  method,  and 
the  results  are  presented  in 
the  abstracts,  where,  for  con- 
venience, the  resulting  cor- 
rections due  to  the  figure  or 
net  adjustment  have  been  add- 
ed. The  latter  computation 
involved  29  conditions  which 
had  to  be  .satisfied.  Here 
weights  to  the  directions  were 
introduced,  depending  upon 
the  same  principle  as  ex- 
plained in  the  case  of  the  ad- 
justment of  the  Epping  base 
net.  In  accordance  with  the 
method  of  application  of 
weights  to  the  directions  in  a 
net  adjustment,  we  derive  the 
mean  error  of  a  triangle  from 
the  sum  of  the  squares  of 
the  closing  errors  of  the  30 
triangles    involved   and    find 

/91 '  I 
y  =zti"'74;   hence  also 

the  probable  error  of  a  direc- 


JD  Grassj 

y^       /        \                                   '\' 

^                                                            /      /                                            \                                                          '- 

^,             //           \           ^ 

c^_Pine  Log                  /                              \ 

1\           ^^/r---_                \ 

1             \                        /           /                                                       ,-^;^  / 

Sa wnee 

1         '^X  /  .^^^y^             / 

\ 

\  Sweat  Mt.)!:^^ 

\        1         //^C~~~~~~~~^                          / 

\ 

1    './^        V^nT^^^^^^^ 

\ 

}j^KeTiesaw             \     \    ^v                / 

^^_^    \ 

AcademY 

Atlanta  Middle  Base    \i^     \ 

I  Northeast  Base 

Atlanta  Southwest  Base^^^^^^^^       X\    \ 

/ 

Kilometers                                     ^^^i:^^     xs\ 

/ 

5            0            5            10          15                                  ~**^oi. 

Statute  Miles                                                 ^ 

tS Stone  Mt. 

6                    0                   5                   10 

1 

tion,  0*674 


/gri 

V  180 


±o"'48.     Further  we    have  the  average  value  of    the  probable 


error  of  a  direction  derived  from  the  measures  and  given  in  column  4  of  the  ab- 
stracts of  directions=±o"'i9,  whence  the  .square  of  the  triangle  combination  error 
f^''^  (o"'48)"  — (o"'i9)"  =  o""2o  nearly.  This  value  was  added  as  a  constant  to  each 
previou.sly  deduced  square  of  the  observing  error;   hence  *"  =  f,"+f-  and  the  weight  of 

each  direction,/)  = —  .     The  reciprocals  of  these  values  after  division  by  o"22' for  the 

sake  of  convenience  are  tabulated  further  on. 


BASE   LINES    AND    BASE    NETS. 


11 


Abstracts:  of  horizontal  dircdions  at  stations  fonnin^  t/ic  .Itlunta  luise  net,  /87^-/874. 

Atlanta  A/iddtr  /;asc*  De  Kalb  County,  Georgia.     January  ii  to  30,  1873.     C.  O.  Uoiilc-lle,  obser\-er. 
75""  direction  theodolite  No.  i.     Circle  used  in  VII  positions. 

Resulting  direc-  .■\pproximate        Correction  Final 

objfc'ls  ohservtd.  tions  from  .station  jirobaWe  from  figure  seconds 

adjustment.  error.  adjustment. 


Number  of 
directions. 


Atlanta  Northeast  Base 
Stone  Mountain 
Atlanta  Southwest  Base 


o     00     00  '000 
So     14     23  -381 

I  So     00     00  '037 


// 
rO  '12 

o  '14 

o  -12 


-  o  -078 

-0193 
01 15 


59  922 

23  '574 
59^922 


Mean  correction     o  '000 
Probable  error  of  a  single  observation  of  a  direction  (/J.  and  /v*.  j,  ('2  =  d=o"'75. 

Atlanta  Sout/iivcsi  Basr,  De  Kalb  County,  Georgia.     Fetiruary  10  to  22,  1S73.     C.  O.  Boutelle,  observer. 
Instrument  as  before.     Circle  u.sed  in  VII  positions. 


5 

Kene.saw 

0 

00 

00  -000 

±015 

—0  -026 

00   026 

6 

Sweat  Mountain 

34 

24 

39  '322 

0  14 

-0130 

39    192 

4 

Atlanta  Middle  Base  and  North- 

east Base 

118 

38 

10  '842 

0  -12 

-0-114 

10  -728 

7 

Stone  Mountain 

184 

22 

33  "046 

0  -II 

^0-219 

33  265 

Atlanta,  City  Hall  spire 

271 

16 

31  "46 

Atlanta,  Capitol  flagstaff 

273 

14 

57  -oS 

Mean  correction     o  "ooo 
Probable  error  of  a  single  ob.servation  of  a  direction  {D.  and  A'. ),  c,  =  ±o"'68. 

Atlanta  Northeast  Base,  Gwinnett  County,  Georgia.      February  27  to  March  21,  1S73.     Observer  and 
instrument  as  before.     Circle  used  in  VII  positions. 


12 

Stone  Mountain 

8 

Atlanta  Middle  Base  and  South- 

west Base 

9 

Kenesaw 

10 

Sweat  Mountain 

II 

Sawnee 

13 

Academy 

±015 


-o  ■082 


O       00       00  "000 

82  49  01  -328 
129  23  28-311 

■56  57  34 '651 
222  15  52 -S40 
293  13  58-560 

Mean  correction     o  -000 
Probable  error  of  a  single  observation  of  a  direction  {P.  and  R.^,  i\  =  zto'^-go. 


00  -0S2 


0 

13 

^0371 

01  -699 

0 

14 

-0-904 

29-215 

0 

15 

-i-o  070 

34721 

0 

'7 

— o-6oi 

52  239 

0 

16 

0-826 

57  734 

*This  station  was  occupied  eccentrically  oni-0423  off  the  line  connecting  Northeast  Base  and  Southwest  Base  and 
the  above  directions  are  reduced  to  the  line. 


78 


THE    EASTERN    OBLIQUE    ARC. 


yihs/racts  of  horizontal  dimiioNS  at  stations  foriiiinff  the  Atlanta  base  net,  /Syj-/S/./ — continued. 

A'r/wsaic.   Coblj  County,  Georgia.     June  25  to  July  18,  1873.     F.  P.  Webber,  observer.      Instrument  as 

before.     Circle  used  in  VII  positions. 


Number  of 
directions- 

Objects  observed 

x6 

.Sweat  Mountain 

17 

Sawnee 

15 

Atlanta  Northeast  Base 

14 

Atlanta  Southwest  Base 

18 

vStone  Mountain 

Carnes 

Lavender 

19 

Pine  Log 

Re 
tioi 

a 

suiting  direc- 
s  from  station 
djustment. 

Approximate 

probable 

error. 

Correction 
from  figure 
adjustment. 

Final 
seconds. 

0 

/ 

// 

/  f 

/' 

// 

0 

00 

00  '000 

±0  "20 

+0  -049 

00  -049 

4 

36 

07  -630 

0'20 

+0  ■!  10 

07  740 

50 

"3 

37  '342 

0-28 

+  0  -226 

37  -568 

64 

50 

59-613 

0-27 

+  0  -290 

59  '903 

66 

36 

1 1  -903 

0-24 

—  I  '056 

ID  -847 

224 

20 

15  '036 

0-36 

15  '063 

252 

07 

00  -675 

0-54 

00  702 

303 

37 

21  -586 

0-41 

+  0  -543 

22  -129 

Mean  correction  +0  '027 
Probable  error  of  a  single  observation  of  a  direction  {D.  and  R. ),  c,  =  ±1"  "Si. 

Sivcat  Mountain ,  Cobb  County,  Georgia.     September  10  to  October  3,  1873.     F.  P.  Webber,  observer 
Instrument  as  before.     Circle  used  in  VII  positions. 


O     00     00  "000  rto'ii  -l-o'oi6  00 '016 

32  34  43  "053 

100  54  55  -825 

145  16  24-035 

186  42  56  -639 

236  54  39  ■''546 

257  37  42  923 

266  39  06 ■ 6 1 6 

279  15  3S'2'S9 

Mean  correction  — o  '036 
Probable  error  of  a  single  ob.servation  fif  a  direction  (  />.  and  R. ),  i\  =  ±r"  '25. 

Stone  Mountain,  De  Kalb  County,  Georgia.     December   ii   to  December  20,  1873.     C.   O.   Boutelle, 
observer.     50"'"  direction  theodolite  No.  3.     Circle  used  in  XI  positions. 


22 

Kenesaw 

Carnes 

26 

Pine  Log 

25 

Grassy 

23 

Sawnee 

27 

Academy 

21 

Atlanta  Northeast  Base 

24 

Stone  Mountain 

20 

Atlanta  Southwest  Base 

0 

1 1 

-|-o  '016 

0 

•26 

0 

■21 

-0-273 

0 

■18 

+  0-529 

0 

21 

+0  -669 

0 

•27 

—  I  -131 

0 

■25 

-0  -835 

0 

■19 

+0-916 

0 

■18 

-0-183 

55 

■552 

24 

■564 

57 

30S 

3« 

■7>5 

42 

-oss 

07 

•532 

38 

-106 

38 
36 

35 
39 
37 
40 

41 


Spire  near  flagstaff 

Kenesaw 

Atlanta  Southwest  Base 

Atlanta  Middle  Ba.se  * 

Sweat  Mountain 

Atlanta  Northeast  Base 

Sawnee 

Academy 

Alcova 


0 

00 

00  -QOO 

rbO-23 

40 

54 

49  -578 

0  -26 

-0-375 

49  '203 

43 

32 

1 1  -836 

0  -19 

-0-245 

II  -591 

58 

02 

13  -204 

0-17 

-0-314 

1 2  -890 

60 

57 

46  -579 

0-24 

+0-915 

47  '494 

74 

58 

48  -469 

0  -10 

—0  -649 

47  -820 

103 

57 

45  -410 

0-14 

+0  -627 

46  -037 

145 

43 

1 7  '505 

0  -20 

+0-119 

17  -624 

207 

54 

55  '333 

0  -21 

Mean  correction  +o-oii 


Probable  error  of  a  single  observation  of  a  direction  {D.  and  R. ),  1?,  =  ±i''-i4. 


*  Result  reduced  to  Middle  Base  in  line,  reduction  ^ 


BASK    LINE.S    AND    HASP",    NETS.  79 

Ahstrach  of  horizontal  dirccliinis  at  ■stations  /'onin)iL;  t/ir  Atlanta  tiasc  net,  /Hyj-/8j4 — continue'!. 

Sawiiec,  Forsyth  County,  Gcorj^ia.  (Jctobcr  7  to  Novenibcr  12,  1^73.  C.  (J.  Houtelle,  obser%'er. 
yjcm  direction  theodolite  No.  r.  November  26  to  December  4,  1873.  Same  observer.  50'"'  direc- 
tion theodolite  No.  3.     Circle  used  in  VII  and  IV  positions,  respectively. 


Number  uf 
directions. 

Objfcts  ohscrvfd. 

A/.inuitli  Mark 

Alcova 

34 

Academy 

31 

Stone  Mountain 

28 

Atlanta  Northeast  Base 

29 

Kenesaw 

30 

Sweat  Mountain 

33 

Pine  Log 

32 

Grassy                          ' 

Blood 

Yonah 

Skitt 

Currahee 

Resulting  direc- 

tioii.s  from  statioi: 

adjustment. 


O  CX)  CK)  'OfJO 

5  59  5"'2"3 

13  35  48'3«6 

3«  56  35  773 

52  13  32  -259 

93  53  42  795 

96  00  32  ■f)S6 

142  50  58  -425 

191  04  26-154 

240  44  00  '564 

263  1 1  38  -044 

273  57  55  '373 

286  (jg  07  '228 


Approximate- 
probable 
error. 


zto  '09 
o  -24 
o  •26 
o  '23 

0  -21 

"■25 
O  '22 

0-I7 

O  -22 

o  -24 
o"3i 

0-32 
O  "22 


Correction 
from  fi;(iire 
adjustment. 


+  0-847 
+  1-311 

-o  -274 
-o  -856 

—0-396 

-o'353 
-o  -244 


Pinal 
.secoiid>. 


49  153 
37  -"^A 
3'  985 
4'  ■9?,9 

31     fXjft 

58  -072 
25  -910 


Mean  correction  -^o  -005 

Ninety-two  series  were  measured  with  theodolite  No.  r,  and  40  with  theodolite  No.  3. 
Proljable  error  of  a  single  observation  of  a  direction  (/?.  and  iV. ),  r,  =  rbi"-34. 

Grassy,   Pickens  County,  Georgia.     Jul}'   13  to  31,   1874.     C.  O.  Boutelle,  observer.     50^^"'  direction 
theodolite  No.  3.     Circle  u.sed  in  XI  positions. 


44 

Sawnee 

43 

Sweat  Mountain 

42 

Kenesaw 

45 

Pine  Log 

Johns 

Cohutta 

Blood 

Skitt 

o     00  00  000 

43     29  35-631 

51     39  33  335 

41  37'o3> 

59  '  7  "050 

183     15  3^^-960 

261     37  28  -061 

297      ;;,  10620 


86 
31 


o  -07 
o  -16 
0-23 
0-13 
o  -26 
o-i8 
0-15 
o  -16 


+0  -228 
+0  -299 
—  r  -40S 
+0  755 


00  •22S 
35  93" 
31  '927 

37  784 


Mean  correction 


Probable  error  of  a  single  observation  of  a  direction  {/).  .uid  R.),e^  =  ±0"  '91. 


So 


THE    EASTERN    OBUOUE    ARC. 


Absfi-acts  of  horizontal  directions,  at  stations  fornun<r  tlie  Atlanta  base  net.  1^7^-18^4 — continued. 

Pine  Loi^,  Bartow  County,  Georgia.     July  29  to  September  17,  1S74.      F.  P.  Webber,  observer. 

,Qcm  repeating  theodolite  No.  32. 


Number  of 
directions. 


49 
48 

47 
46 


Objects  observed. 


Carnes 

Indian 

Coosa 

Lavender 

Gulf 

Johns 

Cohutta 

Grassy 

vSawnee 

Sweat  Mountain 

Kenesaw 

Lost  Motintain 

Pine  Mountain 


Resulting  direc- 
tions from  station 
adjustment. 


O  00  00  '000 

22  30  38  -597 

36  17  34-507 

46  28  35  -508 

70  19  50  '280 

84  39  43  ■143 

141  29  12  '849 

193  10  40  009 

23S  15  36-125 

285  37  II  -880 

30S  19  38-586 

323  54  52-071 

347  59  11-443 


.Approximate 

probable 

error. 


Correction 
from  figure 
adjustment. 


zbo  'ID  

0-13  

O  '12  

o  -08  

012  

O  '12  

o  '14  .... 

o  '13  — o  '600 

o-ii  +0-598 

OT2  -— 0'54I 

o-io  +0-542 

0-15  

0-14  

Mean  correction      o  '000 


Final 
seconds 


39  -409 
36-723 
1 1  -339 
39  •  1 28 


Observations  made  in  sets  of  3  D.  and  3  R.  measures. 

Probable  error  of  a  single  observation  of  a  direction  (6  repetitions),  4',  =±1"  -23. 

Academy.  Gwinnett  Count}-,   Georgia.      December  4  to    10,   1874.     C.  O.  Boutelle,   observer. 
50^"'  direction  theodolite  No.  3.     Circle  used  in  XI  positions. 


53  !  Stone  Mountain 

50  ^  Atlanta  Northeast  Base 

51  vSweat  Mountain 

52  Sawnee 


o     00     GO  -coo 
42     29     26  -166 

65     30     02  -687 


rfco  -lO 
o  -14 
o  -16 
O  '22 


— o  -716 

+  1-837 

-  o  -061 

—  I  -167 


112       53       42-731 

Mean  correction  — o  -027 
Probable  error  of  a  single  observation  of  a  direction  (  P.  and  R. ),  <'i  ^±0"  -95. 

ATI,.A.NTA    BASE    NET    ADJUSTMENT. 

( Ibscrvation  equations. 


I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 


o=+o-o37-   (2)+   (T) 

o=-o-225^  (2)+  (3)-{35)  +  (37)-(i2)+  (8) 
o=-o-2i9-  (4)+  (7)-(36)  +  (37)-(i2j+  (8) 
o=-o-4ii-  (6)+  (7)-(36)  +  (39)-(24)  +  (2o) 
o=-o-367-  (6)+  (4)-  (8)  +  (ioj-(2i)  +  (2o) 
o=  +  r-4To-(i4)  +  (i8)-(38)  +  (36)-  (7)+  (s) 
o=^o-733-(i5)-h(i8)-(38)  +  (37)-(i2)+  (9) 
o=-o-284-  (5)+  (6)-(2o)  +  (22)^(i6)  +  (i4) 
o=  +  2-497— (io)  +  (i3)  — (5o)  +  (5i)-(27)+(2i) 
o=-4-228-(37)  +  (4i)-i53;  +  {5o)-(i3)  +  (i2) 


59  -284 
28  -003 
02  -626 
41  -564 


BASK    LINKS    AND    BASK    NKTS. 


XI 

XII 

XIII 

XIV 

XV 

XVI 

XVII 

XVIII 

XIX 

XX 

XXI 

XXII 

XXIII 

XXIV 

XXV 

XXVI 

XXVII 

XXVIII 

XXIX 


Obscrvalion  equations — continued. 

o=-f2-33i-(38)  +  (4o)-(3i)  +  (29)-('7)  i  (i«) 
o=  +  i-97r-  (9)  t-(ii)-(28)  +  (29)--(i7)  +  (i5) 
o=+4-35r"(iO-!  (i3)--(5o)  1(52)     (34)  I  {28) 

0=  +  2-296~(l0)  +  (ll)-(28)-|-(30)"(23)-j-(2l) 

o=+o-.54-(48)  1  (47)-(26)  I  (23)-(3o)  +  (33) 

0=  -I  •S3i-(33)  +  (32)  -  (44) -f- (45)     (49)1(48) 

0=  -I  •3I3-(26)  +  (25)-(43)^-(45)-(49)^-(47) 

o=-o-3oi-(22)  +  (26)-(47)  +  (46)-(i9)4-(i6) 

0= +0-152-0 -095(4) -1-0 -095(7) -0-026(8) -Ho -026(12)- 1  •505(35)+o -814(36) -0-691(37) 

o=+3-i24— o -I  i6(4)-(-o -021(6) -I  0-095(7) +o-53i(2o)+o -795(21)  -i  -326(24)^0 -344(36) 

+o-499(37)-o -843(39) 
o=+9  -942—0  -226(8) +0  -i99(9)+o  -o27(  12) -7  -676(  14)^0  -798(  15)-  6  •878(  18) 

-4  -941(36)^1-0  -344(37)+4  -596(38) 
o=+o  -436+0  -140(8)— o  -i99(9)+o  -o6o(  io)+o  -699(  14) -o  -798(  15  )-^o  •o99(  16) 

-0-565(20)^^0 -531(21) +0-034(22) 
o=+2-oo4+i  -883(21)^1  -326(24)-o-557(27)+o -917(37)     o -,S43(  39) -o -074(4  r) 

+o-726(5o)-o -496(50-0 -230(53) 
o=— o  -915— o-9i6(  15)  I  o-207(  r7)+o -709(18)— I  -I2S(  2S)->-o  •237(  29)  -  o -892(  31 ) 

-o  ■692(37)+o  -311(38)  I  o  -380(40) 
o=  +  2 -359+0  •628(28)-o -892(31  )+o -264(34 )  +  o -306(37)  -o -380(40) +0 -0741  41) 

-0-305(50)  |-o-o75(52)+o -230(53) 
o=  — 2-792+0-403(9)— 0-500(10) +0-097(1 1  )i-o- J 76(15)^2 -439(16) -2 -616(17) 

+o-22o(28)-5-705(29)+5 -485(30) 
o=+o-463  f  0-223(23 ) -0-238(25 ) +0-016(26  ) -0-222(43 ) -^0-210(44 )+() -012(45) 

+0 -194(47  )-o-4o4(48)+o -210(49) 
o=  +  i  -619-2 -7557(i6)  +  2-6i57(i7)+o-i4oo(i9)+5 -7048(29) -5 -9022(3o)+o -1974(33) 

-ro-5032(46)     0-6971(47)  [0-1939(48) 
o=+5 -491-2  •6i57(i6)  +  2-6i57(  17) -o-42i2(22)+o-42i2(25)-^5-7048(29)-5  -6861 130) 

— o-oi87(32)  +  i  -8885(42)-2 -I  io4(43)+o -2219(44) 


Equations,  of  corrctativc's. 


(i)  =  i-o(+C,) 

(2)  =  i-o(-C,-C.) 

(3)  =  i-o(+C.) 

(4)  =  i  ■o(— C3  +  C5— o  -095  C,5-o-ii6  C;o) 
(5-)  =  i-o(  +  C6-C8) 

(6)  =  i  -o(-C4-C5+Cs+o-02i  Co) 

(7)  =  i  •o(+C3+C4-C6+o-o95  0,5+0-095  C^o) 

(5)  =  i  ■o(+C=  +  C,-C5-o-o26  0,5-0-226  0=,+o-i4o  C™) 
(9)  =  i  •o(+C7-C„+o -1990=,     0-199  0,-+o -403  C=6) 

(  Io)  =  l  •o(+05  — 05  —  0,4-1^0  -060  0,.;  — O  -500  Oae) 

(ii)  =  i  •"(  |-0„-C„+C,4+o-o97  0.6) 
4192 — No.  7 — 02 6 


I 


82 


THE    EASTERN    OBLIQUE    ARC. 


Equations  of  conclati2<es  —continued. 


-, 

t 

p 

(i2):.=  r 

•o(- 

(13)= I 

•o(- 

(I4)  =  i 

■A' 

(15)  =  ' 

•3(- 

(i6)  =  i 

•!(' 

{i7)  =  r 

•I(- 

(iS)  =  i 

•2(- 

(I9)  =  i 

•7( 

(20)  =  I 

•o(- 

(2I)  =  I 

■2(- 

(22)  =  I 

•o(' 

(23)  =  i 

■'( 

(24)  =  r 

•o( 

(25)  =  i 

■o(- 

(26)  =  I 

•I( 

(27)  =  I 

•2( 

(28)  =  I 

•I( 

(29)  =  I 

•2( 

(30)=! 

■I( 

(3')  =  ' 

•I( 

(32)  =  i 

•I( 

(33)  =  i 

•o( 

(34)  =  i 

•2( 

(35)  =  i 

•o( 

(36)  =  i 

•I( 

(37)  =  i 

■o( 

(38)  =  ! 

■2( 

(39)  =  i 

•2( 

(4o)  =  i 

•o( 

(40  =  1 

•I( 

(42)  =  I 

•I( 

{43)  =  i 

■o( 

(44)  =  i 

•o( 

(45)  =  i 

•o( 

(46)  =  I 

•o( 

(47)  =  i 

■o( 

(48)  =  i 

•o( 

(49)  =  i 

•o( 

(5o)  =  i 

•o( 

(50  =  ! 

•o( 

(52)  =  ! 

■I( 

(53)=i 

■o( 

-C-C^-C^+Co+o  -026  C+o  -027  C) 
.-C,-C,„-fC.3) 

-C6+C3-7  '676  C2,+o  -699  C) 

-Cj  +  Co+o  -798  C,,— o  -798  C22— o  -916  €24+0  -176  Cj6) 
-Cs+C.s-o  -099  C2J+2  -4394  C,6— 2  7557  C,8— 2  -6157  C^,) 
-C,.  —  C,c^ 0-207  0,4-2-6157  €36  +  2-6157  C=8+2-6i57  C25) 
+C6+C,+C„+6-87S  C..+0-709  C.4) 

Cs+o  -1400  Cjg) 

C4+C5-C8+0-531  0.0-0-565  C\,) 

C5+C,+C,4+o-795  C.0+0-531  C..+  I  -883  C.3) 

Cg— C,si+o-034  0,2—0-4212  C29) 

C,4  +  C,5  +  0-2230C.,) 

04-1-3260,0-1-3260=3) 
+0,7-0  -2385  O27+0  -4212  O25) 

0,5-0,7+0,8+0-01550,-) 
-09-0-5570,3) 

-0„+0,3-0,4-I    -128  0,4  +  0-628  0,5  +  0-2200,5) 

+0„+0„+o-237  0,4-5  -7048  0,6+5  7048  0,9+5  7048  C,9) 
+0,4-0,5+5  -4S51  0,6-5  '9022  0,s-5  '6861  0,9) 

—  0,,+o  -S92  O24— o  -892  0,5) 
+0,6—0-01870,9) 
-;  0,5— 0,6+0-1974  0,8) 
— 0,3-1-0-264  0,5) 
-0,-1-5050,9) 

-0,-044-06+0  -814  C,9+o  -344  0,0-4  '941  C„) 

+0,+03+07-0,„+o  -691  0,9+0  -499  C,o+o  -344  0„+o  -917  0,3-0  -692  0,4+0  -306  0,5) 
-06-07-0„+4  -596  0,,+o  -311  0,4) 
+04-0-843  0,0-0 -8430,3) 
+0„+o  -380  0,4—0  -380  0,5) 
+0,0—0  -074  0,3+0  -074  0,5) 
+  1-88850,9) 

—  O17— O  -2219  O27— 2  -1 104  O29) 

—  0,6+0  -2097  0,7+0  -2219  O29) 
-1-0,6+0,74-0-01220,7) 

+  0,8  +  0-5032   0,8) 

+  0,54-0,7-0,8+0  -1939  0,7-0  -6971  Cs) 

—  0,5  +  0,6—0-4039  0,7^0-1939  0,3) 

—  0,6—0,7  +  0  -2100  0,7) 

-09  +  0,0-0,3  +  0  -726  0,3-0  -305  0,5) 
+  09  +  0-4960,3) 
+  0,3  +  0  -075  O25) 

—  0,0—0  -230  O23+O  -230  0,5) 


I 


BASK    LINES    AND    BASE    NETS. 
Normal  iyuatio>is. 


B3 


l_ 

C, 

C2 

C3 

C4       C5 

C6        C7          C8          C9     Cio 

•C.i       C12       C13       C14      C15       C16 

C 

7      C,8 

c. 

I 

0- 

=  +0-037 

+  2 

+  1 

2 

-0-225 

+  6 

+  3 

—  1 

+  2                                       -2 

+2-144 

3 

—0-219 

+6-1 

+  2-1     —2 

-2-1     +2                                          —2 

— o'o664 

4 

—0-411 

+6-3   +2 

—  2-|                     —2 

—0-8004 

5 

-0-367 

+6-2 

—  2          -2-2 

—2  "2 

—0-069 

6 

+  1-410 

+6-7     +2-4    —2-2 

+  2-4 

+0-S004 

7 

+0-733 

+  6-7                                     -2 

+  2-4    -2-3 

+0  -665 

8 

-0-2S4 

+6-3 

—  2-1 

<; 

+  2-497 

+  6-4    -2 

+  2          +2-2 

10 

I  r 

-4-22S 
+  2-331 

+6- 

—  2 

+  6-8    +2-3 

-0-665 

12 

13 

+  1-971 
+  4-35' 

+6.7    -2-1    +2-1 
+  6-4    -2-1 

14 

+  2-295 

+  6-5    -2-2 

I,S 

+0-154 

+  6-3  -2 

+  2- 

1    —21 

16 

-.■831 

• 

+6-1 

+  2 

17 

-1-313 

+6- 

I    —2-1 

18 

-0301 

+6-9 

'9 

+0-152 

+3  ■4907'^ 

20 

+  3 '"24 

21 

+  9 '942 

22 

+  0436 

23 

+  2-004 

-M 

-0-915 

25 

+  2-359 

26 

-2-/92 

27 

+0  -463 

28 

+  1  -619 

29 

0- 

=  +5-491 

C=5 


C=6 


Cj3 


499 

3316 

541 

560 

2834 

499 

510 

954 

499 


+0  -954 


-67287 
■05354 


0-091 

5-5261 

5 '435 1 

0226 

6  5145 

2-217 

9-2112 


-     0-317 
+     2  -7384 
+     0-8384 


-  4-17989 

—  I  -69S02 
+  180-71371 


+  0-140 
+0140 
-0'565 
—  I  2822 
o  -838S 
+0  -8384 
+ 1 -32S9 
+0  -5772 


-0-S384 


+0-5772 


+0  -0749 
— o -00364 
+0-20656 

-7-33772 
+  2-14648 


+0-917 
+0-917 
+0-3144 
-2-2596 

+0-917 

+  1  -706 
-o  '0424 


—0-726 

+2-2596 


+0  -63365 
+4-86502 
+0-31545 
+  1  -19985 

+8- 91 109 


-0  '692  +0  -306 

-0-692  +0-306 


+0-4776 
+0  -9764 


+0-692 
— 00669 
+0-1067 
—  I  -2408 
+  1  -240S 


—0-47817 
-0-34531 
+6  -37872 
+  0-95026 
-0-63456 
+4 '82271 


+0  -306 

+o'3C'5 

-  0 -7596 
+0'6oi2 
— 0-690S 
+0-7615 

-  o  -690S 


+  0-21 145 
+  0-15269 
+  0-10526 

+0  -00025 

-2  "01060 
+  1  -78SS6 


-  o  -500 

+  0-1742 

-  2 -6S29  ' 
+  0500 

-  3-9684 

-  4-2876 

+  0-145 

+  6-3885 

-  6-0335 


+  2-6829 


+  0-2627S 

—  0-02717 

—  2  -70072 
+  0-1319S 
+S6  -73579 


-0-2453 
+0-82605 

-0-8:14 

'-0 '03755 
—0-17685 


+0  -45004 


+  3  03127       +   2-4560: 


+  3-96849 

+  3-96849 

-  6  49242 
+  5 '79582 

-  0-0035 

-  06971 

-  2-06877 


+  3-96S49 

+  3-96849 

-  6-25471 
+  6-25471 

-  0-24247 
+  2-5316 

-  2-45607 


—  0-30010   —  0-29917 
+  2-2lS04   +  2-jiSo4 

-89-58581  -87-90629 
-  0-21348  +  0-41457 

+94  -10164   +91  -42321 
+9S  -45205 


84                                                THE  EASTERN    OBLIQUE    ARC. 

Resulting-  Correlates. 

Ci  =— 0-II5  09  c,i=+o-o83  78  C2,  =  — 0-137  98 

Co  =+0-193  iS  C,2=— 0-350  90  Cij=— I  -132  88 

C3  =-0-071  44  C„=---o-982  35  C23=+o-952  70 

C4  =4-0-110  00  C,j=   -1-30571  C24  =  +o-3S3  71 

C5  =-0-378  51  C,5=-o-85i  29  C,5=-i-o46  58 

Ce  =-0-337  23  C,6=-o-234  29  C:;6=+o-755  58 

C7  =+0-050  86  C,7=+o-978  52  C27  =  +o-6S9i5 

C8  = -0-362  70  C:8=— 0-131   58  C28=  +  I'339  40 

C9  =  +  0-411  93  C,9=+o-o8ooi  C2Q=— 0-677  99 

C,o  =  +o-255  74  C2o=  — 1-72674 

and  resulting  corrections  to  observed  directions: 


(I)  = 

=  -0-1151 

(ii)  = 

=  — 0  -6010 

(21)  = 

=  -0-8348 

(31)  = 

=  -t-i  -3112 

(2) 

—0  -0781 

(12) 

+0  -0825 

(22) 

+0-0159 

(32) 

-0  -2437 

(3) 

+0-1932 

(13) 

—0  -8262 

(23) 

+0  -6689 

(33) 

-0  -3526 

(4) 

—0  -1 144 

(14) 

+  0  -2901 

(24) 

+0-9164 

(34) 

+0  -S473 

(5) 

+0  -0255 

(15) 

+0-2258 

(25) 

+0  -5286 

(35) 

-0-3136 

(6) 

-0-1304 

(16) 

+0  -0491 

(26) 

—0-2729 

(36) 

-0  -2452 

(7) 

+0-2194 

(17) 

+0  -1102 

(27) 

-I  -1311 

(37) 

—0  -6491 

(8) 

+0  -3708 

(18) 

-I  '0555 

(28) 

-0-2745 

(38) 

-0  -3747 

(9) 

+0  -9042 

(19) 

+0-5427 

(29) 

—0  -8561 

(39) 

+0-9150 

(10) 

+0  -0695 

(20) 

—0  -1826 

(30) 

-0  -3963 

(40) 

+0  -6273 

(41)  = 

=+o-ii86 

(48)  = 

=  +0-5984 

(42) 

—  I  -4084 

(49) 

-0  '5995 

(43) 

+0  -2994 

(50) 

+  1  -8370 

(44) 

+0  -2284 

(51) 

—0  -0606 

(45) 

+0-7526 

(52) 

—  I  -1669 

(46) 

+0  -5424 

(53) 

-0-7156 

(47) 

-0-5413 

We    have    the    probable  error    of    a    direction    of    unit    weight    0-674    /-!=^--^  = 

o'674    /"'^-^  or  dz  o"'62    nearly,  and  since  the    average    reciprocal  of  the   weights   is 
I '07,  the  probable  error  of  an  observed  direction  is  nearly  ±  o"'65. 


T.ASK    LINKS    AND    I'.ASK    NETS. 


85 


No. 


h'csiilliii^  oil 

i;/i-s  and 

sidrs  iif  lln 

■  Allan  h 

/  hasf  II 

■/. 

Btatioiis. 

observed 

angles. 

Correc- 
tion 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

\/i%.  dis- 
tances. 

Di.stances  in 
meters 

0 

/ 

// 

// 

// 

// 

Stone  Mountain 

3' 

26 

36  -633 

—  0  -404 

36    229 

0-1.-8 

3  -970 

276 

I 

9 

338  -478 

Atlanta  vSouthwest  Base 

65 

44 

2  2  -204 

+0  -334 

22  -538 

0-I28 

4  -212 

738 

2 

i6 

320  -68 

Atlanta  Northeast  Base 

82 

49 

01   -328 

+0  -289 

01  -617 

0-128 

4  -249  47" 

6 

'7 

761  -13 

Stone  Mountain 

14 

3" 

01   -368 

-0  '068 

01  -3(X) 

0  -062 

3  -654 

412 

0 

4 

5 '  2  -446 

Atlanta  Southwest  Base 

65 

44 

22  -204 

ho-334 

22  -538 

0  -062 

4-215 

648 

2 

16 

430  -40 

Atlanta  Middle  Base 

99 

45 

36  -656 

-0  -308 

36  -348 

0  -062 

4  -249 

470 

5 

'7 

761  -13 

Stone  Mountain 

16 

56 

35  -265 

-0  -335 

34  -930 

0  '066 

3  -683 

590 

2 

4 

826  032 

Atlanta  Middle  Base 

80 

14 

23  -381 

+0-271 

23  -652 

0  -066 

4-212 

738 

2 

16 

320  -68 

Atlanta  Northeast  Base 

82 

49 

nl  -328 

+0  -2S9 

01  -617 

0  -067 

4  -215 

648 

.3 

16 

430-41 

Sweat  Mountain 

21 

37 

55  -366 

+0  -652 

56-or,S 

0  -192 

3-970 

276 

I 

9 

338  478 

Atlanta  Northeast  Base 

74 

08 

33  '323 

-0-301 

33  -022 

0  -192 

4  -386 

815 

7 

24 

367  -76 

Atlanta  Southwest  Base 

84 

13 

31  '520 

+0  -016 

3'  -536 

0  -192 

4-401 

456 

3 

25 

203  -24 

Sweat  Mountain 

12 

36 

3 1  -673 

—  r  -099 

30  -574 

0-184 

4-249 

470 

6 

'7 

761  -13 

Stone  Mountain 

17 

25 

34  743 

+  1  -160 

35  -903 

0-184 

4  -3S6 

S15 

7 

24 

367  -76 

Atlanta  Southwest  Base 

149 

57 

53724 

+  0-350 

54  -074 

0-183 

4  -609  S72 

2 

40 

726  04 

Sweat  Mountain 

9 

01 

23  ■  693 

+  1  -752 

25  -445 

0-136 

4-212 

738 

2 

16 

320  -68 

Atlanta  Northeast  Base 

156 

57 

34 '65 1 

—0  -013 

34  -638 

"  '1 37 

4-609 

872 

2 

40 

726  -04 

Stone  Mountain 

14 

01 

01  -890 

- 1  -564 

00  -326 

0-136 

4  -401 

456 

3 

25 

203  -24 

Academy 

42 

29 

26-166 

+  2  -552 

28-718 

0  -290 

4  -212 

738 

2 

16 

320  -68 

vSlone  Mountain 

70 

44 

29  -036 

+0  -768 

29  '804 

0  -290 

4  -358 

"7 

9 

22 

809  -61 

Atlanta  Northeast  Base 

66 

46 

01  -440 

+0  -908 

02  -348 

0  -290 

4-346 

400 

3 

22 

202  42 

Academy 

23 

GO 

36  ■521 

- 1  -897 

34  -624 

0  -337 

4-40! 

456 

0 

25 

203  -24 

Atlanta  Northeast  Base 

136 

16 

23  '909 

-0  -S96 

23  -013 

0  -336 

4-649 

026 

S 

44 

568  -38 

Sweat  Mountain 

20 

43 

03  -077 

+0  -296 

03  -373 

0  -337 

4  -358 

117 

9 

22 

809-61 

Academy 

65 

30 

02  -687 

+0  -655 

03  -342 

0-763 

4-609 

872 

2 

40 

726  -04 

Stone  Mountain 

84 

45 

30  -926 

-0  -796 

30  ■  '30 

0  -763 

4-649 

026 

8 

44 

568  -38 

Sweat  Mountain 

29 

44 

26  770 

+  2  -047 

2S-SI7 

0  -763 

4-346 

400 

3 

22 

202  42 

Kenesaw 

T4 

47 

22  -271 

+0  -064 

22  -335 

0  -1 85 

3  -970 

276 

1 

9 

338  -48 

Atlanta  Northeast  Base 

46 

34 

26  -983 

+0  -534 

27-517 

0-185 

4-424 

374 

S 

26 

568  -98 

Atlanta  Southwest  Base 

iiS 

38 

10  -842 

—0  -140 

10  -702 

0  -184 

4  -506 

615 

3 

32 

108-15 

Kenesaw 

16 

32 

34-561 

—  1  -2S1 

33  -28i) 

"•343 

4-212 

738 

2 

16 

320  -68 

Atlanta  Northeast  Base 

129 

23 

28  -3 1 1 

+0  -822 

29-133 

"  -344 

4-646 

394 

5 

44 

299-06 

Stone  Mountain 

34 

"3 

58-891 

—0-274 

58-617 

"  -343 

4-506  615 

3 

32 

l(V>  -15 

Kenesaw 

1 

45 

12  -290 

- 1  -346 

10  -944 

0  -030 

4-249 

470 

6 

,7 

761  -13 

Atlanta  vSouthwest  Base 

175 

37 

26  -954 

-0-194 

26  -760 

0  -031 

4-646 

394 

5 

44 

299-06 

Stone  Mountain 

2 

37 

22  -258 

+0-130 

22  -38S 

0  -031 

4-424 

374 

S 

26 

568  -98 

I, 


86 


THE  e:astern  oblique  arc. 


Resultiyig  angles  and  s/drs  of  the  Atlanta  base  net  -continued 
IS.  Observed  angles.  ^°TJ^ 


Spher- 
ical 


Spher- 
ical 


angles,    excess. 


I<og.  dis- 
tances. 


IKenesaw 
Sweat  Mountain 
Atlanta  Southwest  Base 

j    Kenesaw 

14  I    vSweat  Mountain 

I    Atlanta  Northeast  Base 

I    Kenesaw 

15  ]    vSweat  Mountain 
[  Stone  Mountain 

ISawnee 
Academy 
St<jne  Mountain 

iSawnee 
vStone  Mountain 
Atlanta  Northeast  Base 

ISawnee 
Academy 
Atlanta  Northea.st  Base 

[  Saw  nee 
19  ]    Atlanta  Northeast  Base 
\  Sweat  Mountain 

IvSawnee 
Academy 
Sweat  Mountain 

ISawnee 
Stone  Mountain 
Sweat  Mountain 

iSawnee 
Stone  Mountain 
Kenesaw 

ISawnee 
Atlanta  Northeast  Base 
Kene.saw 

ISawnee 
Kenesaw 
Sweat  Mountain 


64  50  59  -613 
So  44  21  711 

34  24  39  -322 

50  03  37  -342 

102  22  17  '077 

27  34  06  -340 

66  36  1 1  "903 

93  20  53  -384 

20  02  57  'OOI 

25  20  47  -467 

112  53  42731 

41  45  32  -095 

13  16  56  •4cS6 

2S  58  56  -941 

137  44  07  -160 

35  37  43  '953 
70  24  16  -565 
70  58  05  720 

43  46  59  '827 

65  18  iS  -iSg 
70  54  46  -284 

82  24  43  780 

47  23  40  -044 

50  II  43 '207 

57  03  56-313 

42  59  58-831 

79  56  09  '977 

54  57  07  -022 

63  02  55  -832 

62  00  04  '273 

41  40  10  -536 

92  52  24  -529 

45  27  29712 

2  06  49-291 

4  36  07  -630 

173  n  03-361 


+0-241 
+0-199 
— o  -[56 

+0-177 
+0-851 
-o  -835 

—  I  -105 

— o  -901 
+ 1  -290 

+0  -464 

-o  -452 
~o  -509 

-1  -586 
+  1  -276 
+0  -683 

—  1  -122 
-3-004 

— o  -225 

— O  -122 

— o  -670 

-I  -504 
-I  -244 

—  I  -106 

—  I   -800 

-1-707 

-o  -288 

+0  -248 

—  2  -167 
+  1  -002 

-I  -166 

— o  -582 

- '  -505 
+0  -116 

+0  :46o 
f-o  -061 
-o  -653 


59  -854 
21  -910 
39-166 

37-519 
17  -928 

05  -505 

10  -798 

52  -483 

58  -291 

47-931 
42  -279 
3 '  -S'^-iS 

54  -900 
58-217 
07  -843 
42-831 
13  -561 
05  -495 

59  -705 
17-519 
44  -780 

42  -536 
38  -938 
41  -407 

54  -606 
58  -543 
10  -225 

04  -855 
56  -834 
03  -107 

09  -954 
23  -024 
29  -82S 

49-751 
07  -691 
02  -708 


0-310 
0-310 
0-310 

0-317 
0-318 

0-317 
o  -524 
o.  524 
o  -524 

o  -599 
o  -59S 
o  -599 
o  -320 

0-320 
0-320 

o  -629 
o  -629 
o  -629 

o  -668 
0-668 
o  -668 

o  -961 
o  -960 

0  -960 

1  -125 

I  -125 

I  -124 

'  '599 
1-598 
I  -599 

o  -935 
0-936 
o  -935 

0-050 
0-050 
o  -050 


4  -386  815  7 
4-424  374  8 
4  -182  214  9 

4  -401  456  3 
4-506  615  2 
4  -182  214  9 

4  -609  872  2 
4-646  394  5 
4  -1S2  214  9 

4  -346  400  3 
4  -679  227  4 
4  -538  334  2 
4-212  738  2 
4  -536  834  8 
4  -679  227  4 

4-358  117  9 
4  -536  834  8 
4  -538  334  2 
4  -401  456  3 
4-519  739  5 
4  -536  834  8 

4  -649  026  8 
4-519  739  5 
4  -538  334  3 

4  -609  872  2 

4-519  739  5 
4-679  227  4 

4-646  394  5 
4  -683  359  5 
4-679  227  4 

4  -506  615  3 

4  -683  359  5 

4  -536  834  8 

4  -182  214  9 

4-519  739  5 

A  -683  359  5 


Distances  in 
meters. 


24  367  -76 
26  568  -98 
15  213  -00 

25  203  -24 

32  108-15 
15  213  -00 

40  726  -04 
42  299  -06 

15  213  -oo 

22  202  -42 

47  777  -93 
34  540-94 

16  520  -68 
34  421  -90 
47  777  -93 
22  809  -61 
34  421  -90 
34  540-94 
25  203  -24 

33  093  -26 

34  421  -90 

44  568-38 

33  093  -26 

34  540  -95 
40  726  -04 

33  093  -26 

47  777  -93 
44  299-06 

48  234-69 

47  777  -93 

32  108-15 

48  234-69 

34  421  -90 
15  213-00 

33  093  -26 
48  234-69 


BASE    LINES    AND    BASE    NETS. 

/^(■y/i/Zii/t;  (iiii^/is  ivid  sidfs  of  Ihc  .Itlanla  base  net  -conlimieil. 


^7 


26 


2S 


29 


30 


31 


Pitie  Log 
Swt-at  Mountain 
Ivent'saw 

Pine  Log 

vSawnee 

Kenesaw 

Pine  Log 

Sawnee 

Sweat  Mountain 

Grass}- 
Sawnee 
Sweat  Mountain 

Grassy 

Sweat  Alountain 

Pine  Log 

Grassy 
Sawnee 
Pine  Log 

Kenesaw 

Grassy 

Sawnee 


Ob 

'iirvi 

il  ,-ill^h-s. 

Correc- 
tion. 

Si)her- 

ical 
angles. 

Spher- 
ical 

excess. 

I.oK.  <lis- 
lance.s. 

Distances  in 
meters. 

0 

/ 

// 

// 

'  r 

" 

22 

42 

26  706 

t- 1  '084 

27-790 

"•415 

4-182 

214  9 

'5 

213   fJO 

l(X) 

54 

55  '825 

--()•  289 

55  336 

<i  -416 

4  -587 

666  4 

38  696  03 

56 

22 

3'"*  '414 

0  -494 

37  •92') 

0-415 

4  ■516 

nSl     1 

32 

815-89 

70 

"4 

02  -461 

- 0  -056 

02  -405 

'  -383 

4  -683 

359  5 

48 

234  -69 

4S 

57 

>5  '630 

i-o"503 

'6-133 

'  •,3«3 

4  -587 

666  5 

3« 

696  -04 

6n 

58 

46  -044 

')  '433 

45  '6" 

■  ■3«3 

4  -65' 

920   I 

44 

866  -28 

47 

21 

35  755 

I  '140 

34  •615 

0  -918 

4 -5 '9 

739  5 

33 

r)93  -26 

46 

5" 

26  -339 

,-()  -044 

26  -383 

0  -918 

4-516 

084   1 

32 

815  -89 

^5 

4S 

on  -814 

+0  -942 

"I  756 

0  -9 1 8 

4-651 

920   I 

44 

866  -28 

43 

29 

35  -631 

-|-o-o7r 

35  702 

0  -889 

4-519 

739  5 

33 

093  26 

95 

( ):^ 

54  -068 

-1  0-153 

54-221 

0  -889 

4-680 

2S4  r 

47 

•"'94  -33 

4' 

26 

32  -604 

+0-140 

32  744 

0  -889 

4-502 

751  9 

3' 

•"123  79 

43 

12 

01  '400 

.  +0  -453 

01  -853 

0-931 

4-516 

084   1 

32 

815  -89 

44 

21 

28  -210 

-f  0  -802 

29  012 

0-931 

4-525 

240  9 

33 

515-13 

92 

26 

31  -871 

+0  -058 

31  929 

0-932 

4  -680 

284   I 

47 

S94  -33 

S6 

41 

37  "031 

+0  -524 

37  '555 

0-903 

4-651 

920  I 

44 

866  -28 

48 

13 

27  729 

+0-109 

27  -838 

0  -902 

4-525 

240  9 

33 

5'5-i3 

45 

04 

56-116 

-hi-igS 

57 -3 '4 

0  -902 

4-502 

751   9 

3' 

823  -79 

31 

09 

48  -202 

1  -290 

4-502 

751  9 

3' 

S23  -79 

5' 

39 

33  '335 

- 1  -637 

31  698 

I  -290 

4  -6S3 

359  5 

48 

234-69 

97 

10 

43  "359 

+0  -612 

43 '971 

I  -291 

4  -785 

444  9 

61 

016  -17 

29 

48 

57  '408 

0-995 

4  -525 

240  9 

33 

515-13 

115 

oS 

5S  '577 

-1  -142 

59719 

0-994 

4  -785 

444  9 

61 

016  -17 

35 

02 

03  696 

^-2  -161 

05  -857 

0-995 

4-5S7 

666  5 

3S 

696  04 

26 

33 

40-511 

0  -352 

4-6S0 

2S4  I 

47 

>*^94  -33 

S 

09 

57  704 

—  I  -70S 

55  '996 

0  -352 

4-182 

214  9 

15 

213  -oo 

145 

16 

24  '035 

+  0-513 

24  '548 

0-351 

4  -785  444  9 

61 

016   17 

{Kene.saw 
Pine  Log 
Grassy 

1    Kenesaw 
Grassy 
Sweat  Mountain 

Descriptions  of  stations. 

Atlanta  Soutlnccst  Base. — This  station  is  in  De  Kalli  Count\-,  Georgia,  about  \2 
miles  northeast  of  Atlanta,  near  and  to  the  east  of  the  track  of  the  Southern  Railway. 
It  is  sitttated  on  the  northwestern  .slope  of  a  small  hill,  20  meters  from  and  S  feet  lielow 
the  summit.      It  is  100  meters  south  of  Humphrey's  hou.se. 

This  end  of  the  base  has  both  a  surface  and  an  uiulerorouiul  mark..  The  lower 
mark  is  a  hole  drilled  in  a  copper  bolt  in  the  top  of  a  granite  po.st  2  feet  long  and  6 
inches  square.  The  top  of  this  po.st  is  3>^  feet  below  that  of  a  large  granite  monument 
covering  it,  the  upper  mark  being  in  this  ujiper  monument.  The  upper  block  is  3-3  feet 
.square  at  ba.se  and  3  feet  .square  at  top  and  2-5  feet  high;  it  rests  on  a  brick  platforin. 
laid  in  cement,  5  feet  square  and  i  foot  high,  with  hole  i  foot  square  in  center,  through 
■which  the  top  of  lower  monument  may  be  seen.      A  drill  hole  at  the  intersection  of  two 


88  THE    EASTERN    OBUOUE    ARC. 

cross  lines,  in  a  copper  bolt  driven  into  the  center  of  the  top  of  the  upper  block,  marks 
the  station.  Over  the  upper  monument  is  placed  a  granite  shaft  bearing  the  usual 
inscriptions  on  its  faces.  The  station  is  further  defined  as  the  center  of  a  square  whose 
side  is  24"' '75,  each  angular  point  of  the  .square  being  a  drill  hole  at  the  intersection  of 
cross  lines  in  a  copper  bolt  driven  into  the  top  of  a  stone  post  3  feet  long  and  6  inches 
.square  at  top.  The  center  of  each  reference  mark  is  18  meters  from  the  station,  and 
diagonal  grooves  are  cut  in  top  of  each,  with  an  arrowhead  pointing  to  the  station. 

Atlanta  Northeast  Base. — This  station  is  at  a  road  crossing  on  the  Southern  Rail- 
wa\-,  near  Norcross,  Gwiimett  County,  Georgia.  It  is  on  the  west  side  of  the  road  and 
the  west  side  of  the  railroad,  on  the  place  of  J.  H.  Maloney.  The  station  is  marked 
exactly  as  described  at  Atlanta  Southwest  Ba.se. 

Atlanta  Middle  Base. — The  .station  is  in  De  Kalb  County,  Georgia,  upon  a  .small  knoll 
in  edge  of  woods  65  feet  northwest  of  the  Southern  Railway  and  about  a  quarter  of 
a  mile  northea.st  of  the  railroad  .station  at  Doraville.  The  underground  mark  is  the 
center  of  the  mouth  of  a  .short-necked  bottle.  The  surface  mark  is  a  drill  hole  at  the 
intersection  of  cro.ss  lines  in  the  head  of  a  copper  bolt  driven  into  a  granite  post,  i 
foot  square  and  3  feet  long,  with  diagonal  grooves  cut  in  the  top,  one  in  line  with 
the  base  and  the  other  perpendicular  to  it.  The  copper  bolt  with  the  cross  lines  and 
drill  hole  is  placed  at  the  intersection  of  the  grooves.  Aroinid  this  central  monument 
are  l:)uried  four  reference  marks,  two  in  line  with  the  base  and  two  in  a  line  perpendicular 
to  it.  Each  of  the  granite  posts  is  7  inches  square  and  3  feet  long,  and  has  in  its  top 
a  diagonal  groove  with  an  arrowhead  pointing  to  the  station,  from  which  the  center 
of  each  reference  mark  is  5  feet  di.stant. 

Stone  Moiintajji. — This  station  is  in  De  Kalb  County,  Georgia,  on  the  well-known 
movuitain  of  that  name,  about  15  miles  N.  '76°  E.  from  Atlanta,  and  al)out  i  mile  from 
the  po.st-office.  Stone  Mountain,  on  the  Georgia  Railroad,  De  Kalb  County,  Georgia. 

The  .station  is  marked  by  a  copper  bolt  in  the  solid  granite  of  the  mountain. 
Around  the  bolt  the  rock  is  cut  down  to  a- level  in  a  circle  of  ■XiV'^  f^^^t  radius,  the  bolt 
being  the  center.  In  the  periphery  of  this  circle  are  six  equidistant  holes  2,y2  feet  apart 
and  2  inches  deep. 

Acadeiny. — This  .station  is  on  the  highest  point  of  Academy  Hill,  in  Lawrenceville, 
the  county  seat  of  Gwinnett  County,  Georgia. 

The  underground  mark  is  the  mouth  of  a  bottle  3  feet  below  the  surface.  Over 
this  is  a  granite  po.st  30  inches  long  and  7  inches  square,  with  the  letters  U.  S.  C.  S. 
cut  in  top.  Arotuid  the  central  monument  are  placed  four  reference  marks  about 
30°  W.  of  S.,  30°  N.  of  W.,  30°  E.  of  N.,  and  30°  S.  of  E.  The  center  of  the  SW. 
reference  mark  is  4  feet  6  inches  from  the  center  of  the  station,  and  the  center  of  the 
other  marks  is  5  feet  di.stant  from  .station.  In  the  top  of  each  reference  mark  is  a 
diagonal  groove  with  an  arrowhead  pointing  toward  the  station. 

A?;;f.sc77£'.— This  station  is  on  the  highest  part  of  Kene.saw  Mountain,  about  3  miles 
northwest  of  Marietta,  Cobb  County,  Georgia.  The  station  is  reached  by  following 
the  Marietta  and  Cartersville  road  for  about  2>^  miles  from  the  Kenesaw  House,  in 
Marietta,  and  then  following  the  road  which  turns  to  the  left,  near  a  covered  well,  and 
finally  along  the  spur  of  the  mountain  to  the  .sununit.  The  underground  mark  is  a 
cross  in  the  head  of  a  copper  bolt  driven  into  a  hole  drilled  in  the  .solid  rock  2  feet  i^^ 
inches  below  the  surface.      Above  this  is  planted  a  granite  po.st  5  inches  square,  with 


BASE    LINES    AND    BASE    NETS.  89 

f 

I  the  top  projecting  2  inches  alxjve  the  ground.      The  intersectif)n  of  two  cross  lines  in 

the  top  of  the  post  marks  the  station.  Tlie  letters  U.  vS.  C.  .S.  were  also  cut  in  top  of 
post.  The  station  has  three  reference  marks  A,  B,  and  C — these  being  the  intersec- 
tions of  cross  lines  cut  in  the  heads  of  copper  bolts  driven  into  holes  drilled  in  the  rock. 
The  distances  of  these  points  from  the  .station  are  6'65  feet,  i  i'35  feet,  and  ii'iy  feet, 
re.spectivel}-.  The  angles  subtended  at  the  .station  by  lines  from  A  to  B,  B  to  C,  and 
C  to  A  are  170°  59',  47°  06',  and  141°  55',  re.spectively. 

Sweat  Mountain. — This  station  is  in  Cobb  County,  Georgia,  the  nearest  post-office 
being  Woodstock,  almost  4  miles  distant  in  a  direct  line  on  the  Atlanta,  Knoxville 
and  Northern  Railroad.  The  station  is  ow  top  of  the  mountain,  about  i  )^  miles  from 
Mr.  Dial's  hou.se,  and  is  reached  by  following  the  Marietta  and  Cunnning  road  to  a 
point  9^  miles  from  Marietta,  near  Mr.  Garri.son's,  and  then  taking  the  road  along  the 
southeast  ridge  of  the  mountain. 

The  station  is  marked  by  a  copper  bolt  driven  in  a  hole  drilled  in  the  rock  very  near 
the  edge,  and  has  three  reference  marks,  A,  B,  and  C,  which  are  copper  bolts  driven  in 
drill  holes  in  the  mo.st  solid  rocks  available.  The.se  points  are  6"2  feet,  7 '67  feet,  and 
I2"3  feet,  respectively,  from  the  .station.  Taking  the  line  to  Kenesaw,  vS.  48°33'  W.,  a.s 
the  initial  or  zero  direction,  and  measuring  angles  counter-clock-wise,  the  directions  of 
A,  B,  and  C  are  3°  19'  30",  83°  44'  30",  and  231°  12'  30",  respectively. 

Sawnee. — This  station  is  on  the  most  prominent  or  central  peak  of  vSawnee  Moun- 
tain, in  Cumming  Township,  Forsyth  County,  Georgia,  about  2  miles  NH.  of  Cumming 
and  12  miles  from  Buford,  on  the  vSouthern  Railway. 

The  station  was  marked  temporarily  by  a  copper  tack  driven  in  a  stul),  with  similar 
stubs  for  reference  marks.  The  permanent  marks  are  supposed  to  l)e  the  usual  central 
(  marks  with  four  reference  marks. 

Pine  Log. — This  .station  is  on  Pine  Log  Mountain,  Cherokee  County,  Georgia,  about 

7  miles  north  of  Wolf  Pen.     The  station   is  reached  by  going   east   from   Carters\-ille, 

a,  to  Wolf  Pen;  thence  9  miles  to  Moore's  Iron  Furnace;   thence  3  miles  to   Mr.  Lewis' 

house;   thence  to  the  station  on  top  of  the  mountain. 

The  underground  mark  is  the  neck  of  a  jug  2  feet  6  inches  beneath  the  surface. 
The  surface  mark  is  the  intersection  of  cross  lines  on  the  top  of  a  granite  post  5  inches 
square,  planted  above  the  jug,  the  top  of  post  projecting  above  the  ground.  The  letters 
U.  S.  C.  S.  were  cut  in  the  angles  of  the  cro.ss  lines.  Around  the  station  are  four  granite 
reference  marks  .similar  to  the  central  monument,  to  the  north,  east,  .south,  and  west, 
each  distant  6  feet  from  the  station.  In  the  top  of  each  is  cut  an  arrowhead  pointing  to 
the  station. 

Grassy. — This  .station  is  on  top  of  Grassy  Mountain,  3,290  feet  high,  in  Pickens 
County,  Georgia,  about  6  miles  in  a  direct  line  east  of  Jasper,  the  county  seat,  on  the 
Atlanta,  Knoxville  and  Northern  Railroad.  The  station  marks  are  supposed  to  be  the 
usual  central  moiunnent,  and  four  reference  marks  to  the  north,  east,  south,  and  west, 
each  5  feet  distant  from  the  station. 


I 


1 

I 


90  THE    EASTERN    OBLIQUE    ARC. 

6.    THE    DAUPHIN    ISLAND    BASE    LINE    AND    BASE    NET,   ALABAMA,    1 847. 

Locatio)!,  iinnsKrcim  )t/,  and  r<siilti)io-  lon^th  of  the  Dauphin  hland  base  line.  Alabama, 

1S47. 

When  reconnoitering  for  a  primary  base  line  on  the  coast  of  Alabama  and  Missis- 
sippi in  1845,  Assistant  F.  H.  Gerdes  .selected  a  site  on  Dauphin  Island,  and  a  preliminary 
measurement  was  made  with  a  chain  in  1845-46.  The  measurement  was  made  during 
May  and  June,  1847,  by  A.  D.  Bache,  Superintendent  of  the  Coast  Survey.  A  full 
account  of  this  measurement,  and  the  only  one  published,  will  be  found  in  Coast  and 
Geodetic  vSiirvey  Report  for  1889,  Appendix  No.  17,  pages  479-491,  which  permits  of 
giving  less  space  to  it  here  than  would  otherwise  be  demanded. 

This  is  ihti  first  base  line  measured  with  the  Bache-Wiirdemann  contact-level  com- 
pensating apparatus,  .six  meters  in  length,  designed  in  1845,  and  constructed  at  the 
vSurvey  Office  in  1845-46.  A  description  of  this  apparatus,  with  illustrations  of  its  detail 
construction,  is  contained  in  Coa.st  Survey  Report  for  1854,  Appendix  No.  35,  pages  103- 
108,  by  E.  B.  Hunt,  Lieutenant,  U.  S.  A.,  and  Assistant,  Coast  Survey.  This  article 
was  reprinted  in  Coa.st  Survey  Report  for  1873,  Appendix  No.  12,  pages  132-136,  with 
a  supplement  describing  improvements.  The  last  base  line  measured  with  the  apparatus 
was  the  Atlanta  base  in  1873.  ^t  was  compared  in  1877,  but  its  employment  in  the  field 
clo.sed  with  its  u.se  in  1873.  It  was  .superseded  by  an  apparatus  le.ss  complex,  less  ctunber- 
some,  and  more  easily  transported,  using  a  contact  slide,  and  either  with  or  without  the 
principle  of  compen.sation. 

The  average  elevation  of  the  island  is  l)ut  little  more  than  i  meter  above  the  mean 
level  of  the  Gulf.  The  line  pa,s.ses  over  sand,  generally  bare,  but  in  part  it  is  covered 
with  low  grass  or  rushes.  To  prepare  the  ground  for  the  measure  a  number  of  sand 
ridges  had  to  be  leveled  and  a  few  gullies,  cut  by  the  .sea,  had  to  be  crossed.  The  length 
of  the  base  is  io'66  kilometers  (or  6"62  .statute  miles).  Its  terminal  points  were  xnarked 
with  stone  moninnents  and  (so  called)  milestones  were  set  along  the  line.  In  August, 
1852,  a  hurricane  swept  over  the  i.sland,  cau.sing  the  .sea  to  wa.sh  over  the  line  and  disturb 
several  of  the  intermediate  marks  and  the  monument  at  We.st  Ba.se.  Certain  verification 
marks  having  been  recovered,  part  of  the  line  was  remeasured  in  1855  by  Assistants 
F.  H.  Gerdes  and  J.  E.  Hilgard,  and  the  line  was  further  secured  in  1857  by  the  in.ser- 
tion  of  .screw  piles  as  marks.  The  marks  were  recovered  in  1898  by  Assistant 
W.  B.  Fairfield.  The  middle  point  is  in  latitude  30°i4'7  and  in  longitude  88°ii''6, 
with  mean  azimuth  84°  13'. 

The  length  and  compensation  of  the  Bache-Wiirdemann  apparatus  depends  entirely 
on  the  length  and  the  coefficient  of  expansion  of  the  6-meter  iron  .standard  bar,  prepared 
in  1847  and  known  as  No.  i.  It  was  .standardized  by  means  of  numerous  comparisons 
made  between  the  years  1847  and  1882.  The  elaborate  compari.sons  and  determinations 
of  i860,  made  by  Assistant  J.  E.  Hilgard  at  the  Smithsonian  Institution,  are  described 
in  Coast  vSurvey  Report  for  1862,  Appendix  No.  26,  pages  248-255.  The  coefficient  of 
expan.sion  was  found  to  be  o'ooo  01 1  54  for  the  centigrade  .scale  (  or  o'ooo  006  41  for  the 

±4  ±2 

Fahrenheit  scale  j.      The  weighted  (assumed)  mean  of  the  mo.st  trustworthy  ob.servatious, 


ALEXANDER   DALLAS  BACHE   U806-1867). 


BASE    LINES    AND    BASE    NETS. 


91 


namely,  those  of   i860,  1S77,   and    1882  (the  last  by  the  writer),  gave  the  final  value: 
Length  of  the  6-meter  {a  boict)  standard  (No.  i )  at  0°  C.  =  S'gyg  949  meters*,  whereas 

±3 
the  i860  determination  gave  5 '999  941  meters,  the  difference  l)eing  only  8  /^  in  6  meters. 

±2 
It  was  thought  well  to  adhere  to  the  i860  value  as  the  one  in  good  accord  with  the  coeffi- 
cient of  expansion  then  found.  It  was  found  that  the  compensating  bars  or  "tubes" 
uf  the  apparatus  did  not  retain  an  invariable  length  at  different  times,  probably  owing  to 
the  great  length  of  the  apparatus  and  wear  on  the  compensating  lever,  .so  that  for  each 
base  their  length  had  to  be  specially  determined.  At  Dauphin  Island  tubes  i  and  2 
were  intercompared  in  May  and  June,  before  and  after  the  base  measure,  and  tube  2  was 
likewise  compared  with  the  standard  bar.  The  result.s  were,  tube  i  longer  than  tube  2, 
o"''ooo  021  6:  on  May  11  and  12  tube  2,  at  ai)out  23°"6  C,  with  probablv  rising  temper- 

±1  4 
ture,  was  found  equal  to  6""ooo  057   3,  and  on  June  10,  at  aljout  25°'o  C,  with  probably 

del  I    o 
falling  temperature,  tube  i  was  equal  to  6'" "000  064  o.      K<iuating  these   measures  with 

±11   o 
consideration  of  their  weights,  we  get: 

Length  of  tube   i,  6'" '000071  o 

±11  o 
Length  of  tube  2,    6"''ooo  050  3 

dzl  I    o 

The  adjustment  of  the  compensation  apparatus  for  changes  of  temperature  was 
made  in  1846  by  Superintendent  A.  D.  Bache,  with  the  result  that  the  lengths  of  the 
tubes  were  found  practically  invariable  during  the  range  of  natural  temperatures  as  well 
as  at  different  rates  of  change  of  temperature. 

The  probable  error  assigned  to  the  deduced  length  of  the  tubes  maj'  be  taken  to 
include  all  uncertainty  arising  from  the  direct  comparisons  with  the  .standard,  and  that 
of  the  standard  it.self,  but  excluding  uncertainty  due  to  any  imperfect  compensation 
during  the  measure.  The  temperature  of  the  tubes  was  taken  from  three  thermometers 
attached  to  each  tube,  which  gave  an  average  of  30°  "o  C.  during  the  field  operations,  while 
that  of  standardization  was  24° "3  C;  the  probable  error  of  the  length  of  each  tube  was 
accordingly  increa.sed  to  zbo'"'ooooi4  6.  The  maximum  inclination  of  a  tube  during 
measurement  but  .slightly  exceeded  1°;  the  excess  of  length  of  1777th  tube  over  the  west 
end  of  the  base  was  measured  with  a  bra.ss  meter  .scale,  ha^•ing  regard  for  its  tem- 
perature. 


*  For  further  particulars  see  the  account  of  the  length  of  the  Kl  Paso  base  in  Colorado.  1S79,  in  Special    Publi- 
cation No.  4,  "The  Transcontinental  Triangulation." 


92  THE    EASTERN    OBLIQUE    ARC. 

We  have  for  the  length  of  the  base: 

I  776  tubes  of  mean  length  10  656™' 107  6 

I  additional  tube  No.  i  +6*ooo  i 

Excess  of  last  tube  at  west  base  -o"i7i  3 
Correction  to  reduce  to  mean  value  of  a  double  measure  of  97  tubes          +-o'ooo  i 

Correction  for  inclination  of  tubes  —cogs  8 

Reduction  to  half-tide  level  of  Gulf  — o'oo3  I 

Resulting  length  of  base  10  661"' '837  6 

We  have  also  the  following  resulting  distances  from  the  east  end  of  the  base  to  the 
several  so-called  milestones: 

To  first  milestone  i  608'" '01 5  6 

To  second  milestone  3  216032  5 

To  third  milestone  4  824'048  2 
To  fourth  milestone                       '      6  432 '063  9 

To  fifth  milestone  8  040^079  8 

To  west  end  of  tube  1532  9  i92'oo8  i 

To  sixth  milestone  9  648 '095  6 

To  west  end  of  tube  165S  9  948"oo5  8 
To  sixth  and  a  half  milestone  lo  452' 103  7 

The  hurricane  of  Augitst,  1S52,  having  displaced  milestones  V,  VI,  and  VI ^,  as 
well  as  the  monument  at  West  Base,  that  portion  of  the  old  line  between  the  verification 
marks  at  the  east  end  of  tubes  No.  1533  and  No.  1659  was  remeasured  in  Maj',  1855, 
by  means  of  the  4-nieter  contact-.slide  apparatus,*  with  iron  rods,  Nos.  i  and  2.  Their 
lengths  at  o°C.  were:   No.   i,  3"'"999  937  7,  and  No.  2,  3"''999  909  8. 

The  length  remeasured  is  as  follows: 

188  rods  of  mean  length,  at  30°'67  C.  752""25i  8 
I  rod  No.  I,  at  34° '4  C.  4.001  5 

Exce.ss  of  last  rod  over  line-  — o'26o  o 

Reduction  to  sea  level  — o'ooo  2 

Resulting  length  755""993  i  Original  length  of  1847,  755""9977 

A  .screw  pile  was  in.serted  in  the  line  at  a  distance  9  942"' '798  4  from  the  east  end  of 
the  base. 

The  probable  error  of  the  assigned  length  of  the  ba.se  arising  from  the  uncertainty 
in  the  length  of  tubes  is  ±  o"''o25  94;  that  due  to  contact  and  tran.sfer  errors  during  the 
mea.surement  ( which  occupied  seventeen  working  days)  is  cstiniatedat  ±o""""oi^i  yy6 
or  ±  o"'"ooo  42  and  dz  o"""'o82768  or  zJ=  o""ooo  68,  respectively.!  Combining  these  prob- 
able errors,  we  find  the  .scjuare  root  of  the  sum  of  the  squares  =  =bo'""o26o,  which 
equals  jto'uoo  (nearly)  of  the  length  and  corresponds  to  a  logarithmic  difference  in  the 
length  of  O'OOO  001  06.  Hence  the  final  value  for  the  length  of  the  Dauphin  Island 
base,  in  terms  of  the  prototype  meter  =  10  66i"''837  6,  and  its  logarithm  =4*027  832  06. 

zb  '026  o  dz  I  06 


*  For  description  of  this  subsidiary  apparatus  see  Coast  Survey  Report  for  1856   ."Appendix  No  60 

t  An  account  of  the  experiments  for  contact  and  transfer  errors,  Coast  and  Geodetic  Survey  Report  for  1889,  p.  485. 


$< 


BASK    LINKS    AND    BASK    NKTS. 


93 


Spring  Hill 


The  Dauphin  IsliDid  base  iiel  and  results  of  its  adjustment. 

This  net,  as  shown  in  the  figure,  represents  measures  executed  at  two  periods 
widely  differing  in  date.  The  older  work  of  1846,  1847,  1848,  in  charge  of  Assistant 
F.  H.  Gerdes,  which  inckides  the  base  measure,  is  exhibited  in  the  diagram  by  lines  of 
dashes,  while  the  later  work  of  1897-98,  in  charge  of  Assistant  W.  B.  F'airfield,  is 
shown  by  full  lines.  It  was  at  first  the  intention  to  adjust  the  whole  of  the  measures 
at  the  stations  connected 
with  the  base,  but  when  the 
compvitation  starting  from 
the  Atlanta  Base  was  carried 
through  the  adjusted  trian- 
gulation  and  had  reached  the 
Dauphin  Island  Base,  there 
was  found  an  almost  perfect 
accord  between  its  length  as 
derived  from  the  Atlanta  Base 
and  as  measured  directly. 
No  further  adjustment,  there- 
fore, was  demanded  on  this 
account,  but  for  the  triangu- 
lation  to  the  westward  toward 
New  Orlean.s — that  is,  for  the 
old  triangulation — the  three 
stations.  Cat  Island,  Cedar 
Point,  and  Point  aux  Pins, 
required  to  be  brought  into 
perfect  relationship  with  the 
base  and  with  the  position  of 
Fort  Morgan.  There  is  no 
line  from  Dauphin  Island 
East  Base  to  Fort  Morgan  in 
the  old  work,  and  besides, 
the  direction  from  West  Base 
to  Fort  Morgan  is  not  in  har- 
mony with  the  later  measure. 

In  the  fourth  column  of 
the  following  abstracts  of 
directions  the  twelve  correc- 
tions to  directions  numbered  53  to  64  are  those  which  resulted  from  the  adjustment  of  the 
fifth  section  of  the  triangulation  southwest  of  the  Atlanta  Base,  comprised  between  the 
lines  Creagli  to  Pollard  on  the  north  and  Fort  Morgan  to  Dauphin  Island  West  Base  ow 
the  south.  The  corrections  to  directions  numbered  i  to  16  are  those  pertaining  to  and 
resulting  from  the  present  adjustment  of  the  old  measures.  The  ground  at  the  stations 
is  btit  a  few  meters  above  the  level  of  the  Gulf. 

For  the  details  of  the  adjustment  of  the  triangulation   to  the  northward  vii  the 


Point  aux  Pins 


Dauphin  Island  "West  Base 


Fort  Morqan 


BCUometers 


10 
Statute  itiles 


30 


15 


20 


I 


94 


THE    EASTERN    OBLIQUE    ARC. 


No.  15. 


^oirtt  axuc  Pins 


Dauphin  Island  Base  and  of  Fort  Morgan,  see  the  record  and  results  of  the  fifth  and  last 

section  of  the  triangulation  in  Alabama  ( 1 895-1 898  ). 

The  small  diagram  shows  the  adjusted  figure,  or  the  old 
base  net  upon  which  the  survey  to  the  westward  depends. 
An  independent  start  is  made  directh-  from  the  base. 
Respecting  the  position  of  Fort  Morgan,  the  single  tri- 
angle Dauphin  Island  West  Ba.se,  Cedar  Point,  Fort 
Morgan,  from  the  1847-48  measures,  has  been  added 
to  the  other  triangles.  The  measures  at  Fort  Morgan 
in  1847,  by  Assistant  R.  H.  Fauntleroy,  were  made  in 
connection  with  his  okservations  for  azimuth,  and  the 
azinuith  .station  was  occupied  for  the  measure  of  the  hori- 
zontal angles. 


WlBas 


Dauphin,  Islarvd, 


Abstracts  of  liorizoiital  angles  and  dhrcfioiis  at  stations  of  the  Danpliin  Istand  base  net. 


Daupliin  Island  East  Base,  Mobile  Count)-,  Alabama.  February,  1846.  F.  H.  Gerdes, 
Theodolite  No.  6.  Circle  used  in  IV  positions.  January  and  June,  184S.  F.  H.  Gerdes, 
45'^'"  direction  theodolite  No  4.     Circle  used  in  V  positions. 


Number  of 
directions. 


Objects  olxserved. 


Results  froui 

station  adju.st- 

ment. 


Corrections 
from  net  adjust- 
ment. 


observer, 
observer. 


Final 
second.s. 


Dauphin  Island  West  Base 
Cat  Island 
Cedar  Point 


o     00     00  '00 

52     04     29  -67 

103     52     29  -53 


+0  -05 
-0-28 
+0-23 


Pauptiin  Island  East  Base,  reoccupied  August  i  to  30,  1897,  and  March  6  to  9,  1S9S.     W.  B. 
observer.     30""  repeating  theodolites  Nos.  16  and  32. 


Number  of 
directions. 

objects  observed. 

5« 

Dauphin  Island  West  Base 

59 

St.  Elmo 

60 

Daphne 

61 

Fort  Morgan 

Also, 

Dauphin  Island  West  Base 

Point  aux  Pins,  1898 

Middle  Bay  Light-House 

Fort  Morgan  Light-House 

Sand  Island  Light-House 

Results  from  Corrections  from 

station  adjust-  adjustment  of 

ment.  fifth  section. 


0 

00 

00 '00 

+0-23 

Sr. 

51 

20  71 

— 0  "oS 

125 

25 

47  '09 

+0-56 

197 

27 

36  -91 

-071 

0 

00 

00  'GO 

-^-o  -23 

46 

19 

52  -90 

125 

53 

38  -37 

197 

5S 

04  -8 1 

224 

55 

51  '14 

00-05 
29-39 
29-76 

Fairfield, 


Final 
seconds. 


00   23 
20-63 

47  -65 
36-20 

00  23 


BASE    LINES    AND    HASE    NETS. 


95 


Abstracts  of  horizontal  oii^lcs  and  directions  at  stations  of  tlic  Paupliin  Island 

base  net — continued. 


Dauphin   Island  West  Base,  Mobile  County,  Alabama.      Xoveiiiber,    1S47.      !•".   H.   Genles, 


45'"'    direction    theodolite  No.  4.     Circle  used    in    \'   positions.     January,  I.S4.S. 
observer.     Instrument  as  before.     Circle  used  in  III  position.s. 


V.  H 


observer. 
.  Gerdes, 


Nutiiber  of 
directions. 


Dbjects  oliservfd. 

Petit  Bois 
Grand  Batture 
Point  aux  Pins 

Cat  Island 

Cedar  Point 

Dauphin  Island  Ea.st  Base 

Fort  Morgan^ 

Dauphin  Island  West  Base,  reoccupied  September  r   to  6,  1.S97,  and  February  23  to  27,  1S9S.     W.  B. 
P'airfield,  observer.     .50"'"  repeating  theodolite  No.  32. 


K(;sults  from 

station  adjust- 

inent. 

Corrections 

from  net  adju.st- 

ment. 

Final 
seconds. 

0 

/ 

// 

// 

// 

0 

00 

(X)  'OO 

45 

15 

13  69 

81 

33 

33  52 

+0-I4 

33-66 

128 

34 

20-89 

+0-24 

21  -13 

15' 

37 

06  -72 

—0-49 

06  23 

190 

nl 

23  o^ 

+0  -lo 

23  -68 

19S 

,S'^ 

49  75 

Number' of 
directions. 

Objects  oljserved 

Results  from 
station  adjust- 
ment. 

Corrections  from 

adjustment  of 

fifth  section. 

Final 
seconds. 

0 

/ 

// 

// 

// 

Ca.sotte 

0 

00 

00  -00 

Point  au.x  Pins  ,  1898 

46 

29 

59 '46 

.... 



62 

St.  Elmo 

73 

18 

25-29 

+0-17 

25  46 

63 

Dauphin  Island  East  Ba.se 
Baylor's  West  Base,  1892 

151 
156 

5'^ 

G2 

46-46 
3071 

-0-74 

4572 

64 

Fort  Morgan  Quarantine  fla 

gstaff 

15S 

33 

57  -96 

P~ort  Morgan 

160 

56 

oS-79 

+0-56 

09  "35 

Sand  Island  Light-House 

'74 

34 

48  -52 

Horn  Island  Light-House 

333 

3' 

03  -2  I 

fort  Morffan,  Baldwin   County,    Alabama.     March,    1S46,   and   May,  i<S46.      F.  H.   Gerdes,  observer. 


Theodolite   No.  6.     Circle  used  in  III  positions.     December,  1847. 
direction  theodolite  No.  4.     Circle  used  in  \'  positions. 


Number  of 
directions. 


C»bjects  observed. 


Results  from 
station  adjust- 
ment. 


J.  V,.  Hilgard,  ob.server.     45 '" 


Corrections 

from  net  adjusl- 

mcnt. 


F"inal 
seconds. 


53 


Azimuth  Mark 

Dauphin  Island  West  Ba.se 

Cedar  Point 


o  00  00  '00 
65  00  30  -90 
1 15  44  45  oO 


■^o  '45 


*  The  measures  of  theangle  between  East  Base  anr  Fort  Morgan  in  1S4S  and  1S97  differ  3"S4:  probably  the  object 
observed  upon  was  not  well  centered  over  the  station,  'riiedirection  is  not  interlaced  with  other  directionsat  the  station, 
and  no  use  has  beei\  made  of  it  in  the  present  adjustment. 


96  THE   EASTERN   OBLIQUE    ARC. 

Abstracts  of  horizontal  angles  and  directions  at  stations  of  the  Dauphin  Island 

base  net — continued. 


Fort  Morgan,  reoccupied  June  14  to  20,  1S97,  and  January  20  to  23,  1898.     W.  B.  Fairfield,  observer. 
30^'"  repeating  theodolite  No.  16  used  in  1897,  and  30'^"^  repeating  theodolite  No.  32  in  1898. 


Number  of 
directions. 

objects  obs 

53 

Dauphin  Island  West  Base 

54 

Dauphin  Island  East  Base 

Baylor's  West  Base,  1892 

Point  aux  Pins,  1898 

55 

St.  Elmo 

56 

vSpring  Hill 

Middle  Bay  Light-House 

57 

Daphne 

Sand  Island  Light-House 

Results  from 

station  adju,st- 

ment. 

Corrections  from 
adjustment  of 
fifth  section. 

Final 
seconds. 

0 

/ 

// 

// 

// 

0 

00 

00  '00 

-Ho -45 

00-45 

8 

30 

12  -65 

+0-23 

12-88 

10 

02 

56-90 

27 

3^ 

10-50 

55 

51 

43 '92 

—0-23 

43 '69 

73 

56 

39-86 

-0-58 

39-28 

89 

35 

36  -84 

02 

05 

04  -52 

+0-14 

04  -66 

!96 

55 

25-96 

Cedar  Point,  Mobile  Cotmty,  Alabama.     April  23  to  28,  1848.     V.  H.  Gerdes,  observer.     30'"'  theodolite. 
Circle  used  in  III  positions. 


Number  of 
directions. 


objects  observed. 


Results  from 
station  adjust- 
ment. 


Corrections 
from  net  adjust- 
ment. 


Final 

seconds. 


Fort  Morgan 

Dauphin  Island  East  Ba.se 
Dauphin  Island  West  Base 
Point  aux  Pins 


o  00  00  -00 

44  10  49  -67 

81  54  02  -57 

133  36  22  -92 


— o  -07 
+0  -17 

—  O  'lO 


Cat  /stand,  Mobile  County,  Alabama.      April  15  to  16,  1846.      F.  H.  Gerdes,  observer. 
No.  6.     May  19,  1847.     J.  E.  Hilgard,  observer.     May,  1S4S.     F.  H . Gerdes,  observer. 


49  -60 

"2  74 
22  -82 

Theodolite 


14  I  Datiphin  Island  East  Base 

15  Dauphin  Island  West  Base 

16  Point  aux  Pins 


o    00     «]  -oo 

66     28     28  -62 

163     50    05  -99 


+0  -10 
— o  -19 

+0  -ID 


Point  aux  Pins,  Mobile  County,  Alabama.     May  23  to  June  i,  1848.     F.  H.  Gerdes,  observer, 
theodolite.     Circle  tised  in  III  po,sitions. 


II 

12 
13 


I 

II 
III 
IV 

V 


0 

00 

00 -co 

+  0-32 

22 

36 

33  -45 

—0-29 

5« 

14 

08  -33 

^0-03 

105 

51 

21  -51 



147 

05 

47-69 

.... 

00  -10 

28  -43 

06  -09 

30'"' 


00  -32 

33 '16 
08  -30 


Cedar  Point 

Cat  Island 

Dauphin  Island  West  Base 

Petit  Bois 

Grand  Batture 

DAUPHIN   ISLAND   BASE   NET   ADJUSTMENT. 

( '>bscrvation  equations. 

o=-i-oo-(3)  +  (4)-  (5)+  (7)-  (8)+  (9) 
o=  +  i-25-(i)-f{3)-  (9)  +  (io)-{ii)  +  (i3) 
o=-fo-76-(2)  +  (4)-  (5)-f  (6)-(i4)  +  (i5) 
o=-o-65-(i)  +  (2)-(i2)  +  (i3)--(i5)  +  (i6) 

o=-o-4  +1  •63(i3)-2-93(i2)  +  i -30(11)  |  i -66(  10  1-4  •38(9)  +  272(8)-o-52(7)-|-2-i6(5) 
—  I  •64(6)+o-27(i6)-{  o-65(i5)-o-92(  14) 


BASE    LINEvS    AND    BASE    NETS. 


97 


The  solution  of  the  normal  equations  j^ives  the  values  of  the  correlatives: 


and  the  corrections  to  the  directions  are: 


c,= 

+0 

•2645 

c,= 

— 0 

-2234 

C3  = 

— 0 

•1617 

C4  = 

+0 

•0783 

C5  = 

+0 

-0726 

ctions  are: 

// 

// 

(i)  = 

=  +o-i45 

(9)  = 

=  +0-170 

(2) 

+o  -240 

(10) 

-0-103 

(3) 

-0  -488 

(II) 

+0-318 

(4) 

+0-103 

(12) 

—0  -291 

(5) 

+0  -054 

(13) 

—0-027 

(6) 

-0-281 

(14) 

+  0095 

(7) 

+0-227 

(15) 

-0-193 

(8) 

—0  -067 

(16) 

+0  -098 

The  mean  error  of  a  direction,./ — Z3  =  -(-o''  -38  and  the  probable  error=^o"  -26. 
Kc'sulthti^  ang/t's  and  sides  0/  the  Dauphin  Island  base  net. 


stations. 

Obse 

rved 

angles. 

Correc- 
tion. 

»pneri- 

ical 
angles. 

^»pneri- 

ical 
excess. 

I.og.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

'/ 

// 

// 

Cedar  Point      ' 

37 

43 

12  -90 

+0-24 

13 '14 

0  -09 

4-027   832 

I 

10 

661  -83S 

Dauphin  I'd.  East  Base 

103 

52 

29-53 

+0-17 

29-70 

0  -10 

4-228 

357 

0 

16 

918-31 

Dauphin  I'd.  WestBase 

38 

24 

16-86 

+  0-59 

17-45 

0  -10 

4  -034  45S 

5 

10 

825-76 

Point  aux  Pins 

58 

14 

08  -33 

-0  -35 

07  -98 

0  -21 

4  -228 

357 

0 

16 

918-31 

Cedar  Point 

51 

42 

20-35 

—0  -27 

20  -08 

0  -21 

4  193 

605 

I 

15 

617-27 

Dauphin  I'd.  West  Base 

70 

"3 

33  '20 

-0-63 

32-57 

0  -21 

4-271 

975 

5 

1 8 

705  -77 

Cat  Island 

66 

28 

28-62 

—  0  -29 

28-33 

0  -08 

4-027 

S32 

I 

10 

661  -84 

Dauphin  I'd.  East  Base 

52 

04 

29-67 

-0  -33 

29-34 

0  -07 

3  -962 

492 

9 

9 

172  -61 

Dauphin  I'd.  West  Base 

61 

27 

02  69 

-0-I4 

02  -55 

0  -07 

4-009 

213 

8 

10 

214-42 

Point  aux  Pins 

35 

37 

34  -88 

t  0  -26 

35-14 

0  09 

3-962 

492 

9 

9 

172  -61 

Cat  Island 

97 

21 

37  '37 

+0  -29 

37-66 

0  -09 

4-193 

605 

2 

15 

617-27 

Dauphin  I'd.  West  Base 

47 

(X) 

47 '37 

+0-10 

47-47 

0  -09 

4  061 

419 

I 

II 

319 -I  I 

Fort  Morgan  (1S47) 

50 

44 

14-6 

+0-1 

14-7 

0  -2 

4-228 

357 

0 

16 

918-31 

Dauphin  I'd.  West  Base 

47 

21 

43  ■" 

+0-2 

43-2 

0-2 

4  -206 

'43 

7 

16 

074  -73 

Cedar  Point 

81 

54 

02  -6 

+0-2 

02  -8 

"■3 

4  -335 

1 20 

3 

21 

633  -17 

Descriptions  of  Stations. 

Daup/i/n  hla>id  East  Base. — This  station  is  on   Dauphin   Island,  at   the  entrance  of 

Mobile  Bny    about  7  miles  from  the  west  end  of  the  island  and  352  miles  from  the  east 

end,  near  the  western  edge  of  the  pine  woods  which  cover  the  ea.stern  end  of  the  i.sland. 

The  -Station  was  recovered  and  reoccupied  in  1S97  and  marked  as  follows: 

In  a  bed  of  cement  5^  feet  .stiuare,  extending  6  feet  below  the  surface,  are  two 

4192 — No.  7 — 02 7 


98  THE    EAvSTERN    OBLIQUE    ARC. 

pieces  of  drain  tile  2  feet  long  and  4  inches  in  diameter,  each  placed  with  its  axis 
vertical,  one  above  the  other,  the  lower  extending  7  inches  below  the  bottom  of  the 
cement.  A  pine  pole  6  feet  long  and  2  inches  in  diameter  is  driven  down  through  the 
pipes  until  its  top  is  16  inches  below  the  top  of  the  upper  tile.  Above  this  pole  in  the 
upper  pipe  are  placed  vertically,  one  above  the  other,  two  copper  bolts,  each  H  inches 
long  and  3'/(  inches  in  diameter,  a  cross  on  each  bolt  marking  the  station,  the  upper 
mark  beings  feet  l)elow  the  surface.  The  bolts  are  held  in  place  by  cement,  with 
which  the  remaining  space  of  the  pipes  is  filled.  Above  the  top  of  the  upper  pipe  a 
cavity  i  foot  square  and  6  inches  deep  is  left  in  the  cement.  Over  this  cavity,  still 
embedded  in  cement,  the  four  original  granite  blocks  of  the  base  of  the  monument  of 
1847  are  built,  as  originally,  in  two  courses,  the  top  of  the  upper  course  projecting  2 
inches  above  the  surface.  A  copper  bolt  in  the  top  of  one  of  the  blocks  of  the  upper 
course  is  directly  over  the  cross  on  tlie  bolt  in  the  pipe  and  marks  the  station.  Tlie 
original  granite  shaft  is  placed  on  this  foundation  and  cemented  down  over  the  copper 
bolt,  its  apex  again  marking  the  station.  On  the  north,  east,  south,  and  we.st  faces  of 
the  .shaft  are  inscribed,  respectively,  "A.  D.  Bache,  Siiptdt.,"  "  U.  S.  Coast  Survey," 
"  1847,"  "  Base  No.  5."  The  station  is  witnessed  by  two  marks  in  the  same  vertical 
line,  one  on  the  surface  and  one  underground,  in  prolongation  of  th^  base  line,  144' 1025 
meters  east  of  the  extremity  and  just  in  the  edge  of  the  pine  woods.  The  underground 
mark  is  a  cross  in  an  iron  bolt  in  the  top  of  a  tile  pipe  2  feet  long  embedded  vertically 
in  a  mass  of  cement  2  feet  in  diameter,  the  top  of  the  pipe  being  3  feet  below  the  surface. 
Above  this  ])ipe  is  placed  a  granite  block  i  foot  square  and  2^^  feet  long,  the  top  of 
block  being  flush  with  the  surface  and  containing  a  copper  bolt  as  the  surface  mark. 

Dauphin  Island  U^esf  Base. — This  station  is  on  the  western  end  of  Dauphin  Island. 
In  1847  the  station  was  within  one-half  mile  of  the  extremity  of  the  island,  while  in 
1897  the  island  extended  3^2  miles  west  of  it.  In  September,  1897,  the  distance  was 
reduced  by  a  storm  which  wa,shed  away  i  mile  of  the  western  end  of  the  island.  The 
station  is  marked  as  described  at  Dauphin  Island  East  Ba.se,  except  that  the  cement 
at  this  .station  is  6  feet  square  and  5  feet  deep  and  only  one  piece  of  tile  pipe  was  put  in. 

Fori  Morga)i. — The  station  is  near  the  center  of  the  northwest  bastion  (No.  2)  of 
Fort  Morgan,  at  the  entrance  to  Mobile  Bay.  The  station  of  1S46  was  recovered  and 
reoccupied  in  1892  and  again  in  1897-98. 

The  earthenware  vessel  u.sed  originally  was  left  in  its  place,  filled  with  cement,  and 
a  nail  was  placed  in  its  center  to  mark  the  station,  the  top  of  the  nail  being  2^  feet 
below  the  surface.  Aliove  this  was  placed  verticallj'  a  section  of  tile  drain  pipe  inclosed  in 
a  nail  keg,  both  filled  with  cement.  In  the  pipe  are  two  spike  nails,  one  above  the  other, 
making  additional  marks.      The  head  of  the  upper  nail  is  just  beneath  the  brick  floor. 

Cat  Island. — This  station  is  on  Cat  Island,  in  Mississippi  Sound,  north  of  Dauphin 
Island.  The  station  of  1845  was  marked  by  a  buried  earthenware  cone.  In  1855  a  new 
station  was  e.stablislied  near  the  old  one. 

Cedar  Point. — This  station  is  on  Mon  L,ouis  Island,  on  the  western  .side  of  Mobile 
Bay.  The  station  is  situated  on  the  ea.stern  extremit}'  of  the  island,  on  a  narrow  strip 
of  Ijeacli,  among  marshes.  In  1846  an  earthenware  cone  was  buried  as  the  station  mark, 
and  copper  nails  were  driven  in  blazed  trees  with  the  following  directions  and  distances: 
One  northwest,  9  feet  4  inches;  one  northeast,  18  feet;  one  southwest,  32  feet  6  inches, 
as  reference  marks. 


BASE    LINES    AND    BASE    NETS.  99 

Point  aiix  Pi)is. — On  the  point  of  land  of  the-  same  name  which  extends  southward 
into  Mississippi  vSound,  just  west  of  Bayou  Batture.  \\\  1X46  the  station  was  marked  by 
an  earthenware  cone  buried  3  feet  under  the  surface.  In  1848  four  poles  4  feet  lon^ 
and  6  inches  in  diameter  were  inserted  around  the  undisturbed  cone,  the  station  being 
the  point  of  intersection  of  two  perpendicular  lines  determined  by  four  copper  nails  driven 
in  the  tops  of  these  poles. 

St.  Elmo. — The  .station  is  in    Mobile  Count}',  Alabama,  about   2   miles  east  of  St. 

Elmo,  on  the  Louisville  and  Nashville  Railroad,  and  about  one-half  mile  south  of  Otis' s 

mill.     The  station  is  in  the  northwest  corner  of  N.  E.  yi  of  S.  E.  Yx  of  S.  E.  ){  of 

1  S.  E.  ;^  of  N.  W.  X'  •''Cc.  19,  T.  6  S.,  R.  2  W.,  and  is  distant  from  the  northwest  corner 

of  section  19,  3426  feet,  and  bears  from  .said  corner  313°  43'  true. 

The  underground  mark  is  the  intersection  of  cross  lines  on  top  surface  of  limestone 

post,  6  inches  square  and  18  inches  long,  buried  vertical!}-,  with  top  3  feet  below  surface 

^  of  ground.      The  letters  U.  vS.  C.  G.  S.  are  cut  in   the  angles  of  the  cross  lines.     Six 

*  inches  above  this  is  another  limestone  po.st,  6  inches  square  and  28  inches  long,  its  top 

level  with  the  surface  of  the  ground  and  marked  as  the  lower  stone. 

Daphne. — This  station  is  in  Baldwin  County,  Alabama,  about  one-half  mile  northeast 
of  the  court-hou.se  at  Daphne.  The  station  is  in  the  southwest  corner  of  the  S.  W.  ^ 
of  S.  W.  %  of  N.  E.  Yx  of  N.  E.  Y\  of  N.  E.  Ya^  sec.  19,  T.  5  S.,  R.  2  E.  Distance 
from  the  northeast  corner  of  section  19  to  station  is  882  feet,  and  the  station  bears 
S.  44°  17'  W.  (true)  from  the  northeast  comer  of  section  19. 

A    I -gallon  stone  jug  was  buried,  bottom  up,  and  a  small  hole  in  the  center  of  the 

{bottom,  3  feet  below  the  surface,  is  the  underground  mark.  A  limestone  post  6  inches 
square  and  30  inches  long  was  placed  in  a  vertical  position  6  inches  abo\-e  the  jug,  the 
surface  mark  being  the  intersection  of  cross  lines  on  its  top  surface,  which  is  flush  with 
the  ground.  The  letters  U.  S.  C.  G.  S.  are  cut  in  the  usual  manner  in  the  angles  of 
the  cross  lines. 

Sprhig  Hill. — The  station  is  about  7  miles  northwest  of  Mobile,  on  the  highest  part 
of  Spring  Hill,  on  the  land  of  Judge  H.  Anstell,  about  40  feet   north  of  the  fence  line 
of  main  road  and  about  200  yards  west  of  road  going  to  \^'histler,  and  also  about  200 
{  yards  west  of  station  Spring  Hill  on  electric  road. 

The  station  is  marked  as  Daphne,  except  that  the  jug  is  buried  mouth  up,  the 
center  of  mouth  being  the  underground  mark.  The  following  true  bearings  and  dis- 
tances were  measured:  Oak  tree,  No.  i,  N.  62°  33'  10"  E.,  103  feet;  oak  .stump,  No. 
2,  N.  18°  17'  20"  W. ,  39  feet  9  inches;  oak  .stump,  No.  3,  vS.  95''  46'  25"  W..  44  feet 
7  inches;  fence  line,  S.  29°  47'  E.,  39  feet  11   inches. 


lOO 


THE   EASTERN    OBLIQUE   ARC. 


C.       SYNOPSIS  OK  THE    MEASUREMENTS    AND    RESULTS  OF   THE   BASE    IINES   OF    THE  OBLIOUK;   ARC. 


Name  of  line. 


Date  of  measure. 


Chief  of  party 
and  observer. 


No. 


Epping  Base  Me.         1357,  July  and  Aug.  A.  I).  Baclie 

Massachusetts  Base      Mass.     1844,  Sept.  to  Nov.  E.  Blunt 

Fire  Island  Base  N.  Y.      1834,  Aug.  to  Oct.  F.  R.  Hassler 

Kent  Island  Base  Md.        1844,  May  and  June  J.  Ferguson 

I  1872,  Nov.  and  Dec.  | 
1S72,  Dec.  and  1873,  Jan.    [C.O.Boutelle 

1S73,  July  and  Aug.  J 
1847,  May  and  June  A.  D.  Baclie 


Dauphin  Island  Base     Ala. 
Name  of  line 

Epping  Base 
Massachusetts  Base 
Fire  Island  Base 
Kent  Island  Base 
Atlanta  Base 
Dauphin  Island  Base 


.Apparatus  used. 

Bache-Wiirdemann 

Hassler 

Hassler 

Hassler 

Bache-Wiirdeinann 

Bache-Wiirdemann 


Resulting  length  Logarithm  of  .'Approximate 

inme'ersand  preceding  num-       probable  error  in 

probable  error  .  bers.  terms  of  length. 


8   715  -9422  3-940  314  34 

±      158  ±        79 

17  326-3763  4-238  707  74 

d=        35S  ±       90 

14  058  -9709  4-147  953  53 

±585  ±1  81 

8  687  -5446  3  -938  897  05 

±      680  ±  3  40 

9  33S  '4778  3  "970  276  09 
±        222  ±   I  03 

10  661  -S376  4 '027  832  06 

d=    260  :±:  I  06 


„  1 

f 5?0  0  0 


4^T0  0  0 


I¥  0  u  0  0 


15  8  0  0  0 


1 

■J'S'T  0  0  (» 


I 

I 


PART    II. 


THE  MAIN  TRIANGULATION. 


THE  MAIN  TRIANGULATION  BI-:T\V1:i:\  TIIH  BAMi 

LINES  OR  NliTS. 


A.  GENERAL  TREATMENT  OE  THE  REDUCTION  OF  THE  MAIN  TRI- 
ANGULATION BETWEEN  CALAIS,  MAINE,  AND  NEW  ORLEANS, 
LOUISIANA. 

Since  the  earl}-  and  partial  publications  of  preliminar}'  results  of  the  various  parts 
of  this  triangulation,  as  referred  to  in  Part  I,  changes  have  taken  place,  not  only  in  the 
field  work  by  additional  stations  or  measures,  but  also  in  the  office  work  of  compu- 
tation in  respect  to  the  general  treatment,  and  due  to  the  experience  gained  in  the 
meantime.  Nevertheless,  it  was  desirable  to  retain  as  much  as  possible  of  the  older 
reductions,  such  as  the  computations  of  the  base  lines,  the  local  adjustments  of  the 
horizontal  directions,  and  the  adjustment  of  the  base  nets.  That  part  of  the  oblique 
arc  which  is  in  common  with  the  arc  of  the  parallel  of  ^  =  39°  is  retained  unchanged. 

When  dealing  with  the  treatment  of  the  portion  of  the  oblique  arc  traversing  the 
New  England  States,  it  became  neces-sar}'  to  introduce  the  station  Mount  Washington, 
New  Hampshire,  into  the  scheme,  and  to  consider  the  most  advantageous  manner  l)y 
which  the  three  base  lines  (or  their  nets),  the  Epping,  the  Massachusetts,  and  the  Fire 
Island  bases,  could  be  brought  into  perfect  accord.  This  was  to  be  done  with  due 
regard  to  the  labor  involved  in  the  establishment  and  .solution  of  a  large  number  of 
equations.  At  the  same  time  attention  had  to  be  given  to  the  circumstance  of  the 
intersection  of  the  oblique  arc  with  a  triangulation,  now  nearly  completed,  which  can  be 
u.sed  for  the  discussion  of  an  arc  of  the  parallel,  in  latitude  42^4°,  from  Cape  Cod  to  the 
State  of  Iowa,  executed  partly  by  the  U.  S.  Lake  Survey  and  partly  by  the  U.  S. 
Coast  and  Geodetic  Survey  for  this  and  other  purposes.  Further,  attention  had  to  be 
given  to  non-interference  with  the  full  development  of  the  large  triangulation  in  the 
States  of  New  Hampshire  and  Vermont,  which  has  Killington,  Vermont,  as  a  central 
station.  After  due  consideration  it  was  decided  to  retain  unchanged  the  adjustment  of 
the  Epping  base  net  as  made  in  June,  1864,  and  to  adjust  the  triangulation  between 
the  three  bases,  so  as  to  preserve  the  length  of  the  side  Humpback  to  Mount  De.sert 
(of  the  Epping  base  net),  the  Massachu.setts  base,  and  the  side  Wooster  to  Sandford 
(of  the  Fire  Island  base  net).  This  scheme  involves  the  simultaneous  solution  of  57 
equations,  two  of  which  are  length  ecpiations,  each  containing  a  large  number  of  terms. 
The  results  from  the  old  but  less  perfect  scheme  differ  very  little,  and  within  the 
imcertainties  of  the  measures,  from  tho.se  now  obtained,  and  also  indicate  the  excellent 
accord  of  the  relations  of  the  newly  added  station  to  the  surrounding  stations.  The 
small  extension  of  the  Epping  base  net  from  the  side  Cooper  to  Howard  to  the  boundary 
on  the  St.  Croix  River  was  afterwards  treated  by  itself. 

The  .stretch  of  triangulation  between  the  base  nets  of  the  Fire  Island  base  and  the 
Kent  Island   base  starts  from  the  line  Bald  Hill  to  West  Hills,  and  ends  on  the  line 

105 


I04  THE    EASTERN    OBLIQUE    ARC. 

Osbornes  Ruin  to  Turke\-  Point,  and  the  latter  line,  being  a  part  of  the  adjusted  triangu- 
lation  of  the  arc  of  the  parallel  in  (^=39°,  is  preserved  as  given  in  Special  Publication 
No.  4,  "  The  Transcontinental  Triangulation.  " 

The  adjustment  involved  the  solution  of  35  equations,  of  which  the  conditional  or 
observation  equation  for  accord  of  length  of  sides  contains  89  terms.  The  triangulation 
lying  between  the  line  Osbornes  Ruin  to  Turke}'  Point,  Maryland,  and  the  line  Tobacco 
Row  to  Spear,  Virginia,  is  retained  unchanged  as  given  in  Special  Publication  No.  4. 

Upon  reaching  latitude  36°  the  triangulation  splits  into  two  branches,  one,  the 
western  and  later  one,  passing  through  Tennessee,  the  other  and  older  one  through 
North  Carolina.  They  unite  again  in  northern  Georgia.  The  angular  mea.sures  on 
the  western  branch  were  made  with  an  inferior  instrument.  A  study  of  the  local  adjust- 
ments of  this  triangulation  and  of  the  approximate  computations  which  were  available 
indicated  that  the  angle  measures  did  not  pos.se.ss  quite  the  .same  accuracy  as  those  of 
the  eastern  branch  and  could  lend  no  additional  value  to  the  triangulation  to  the  .south- 
ward. Moreover,  there  are  no  astronomic  ob.servations  of  any  kind  connected  with  this 
triangulation.  For  these  rea.sons  the  western  or  Tenne.s.see  branch  was  not  used  as  a 
part  of  the  arc,  and  the  computation  between  the  Kent  I.sland  and  Atlanta  bases  was 
carried  through  the  ea.stern  branch. 

Proceeding  southwestward  from  the  line  Tobacco  Row  to  Spear  to  the  Atlanta 
base,  the  adjustment  was  made  in  three  parts. 

The  complex  strong  figure  between  the  lines  Tobacco  Row  to  Spear  and  Buffalo  to 
Moore  was  first  adjusted  and  involved  the  .solution  of  24  equations.  The  influence  of  the 
Atlanta  base  was  then  extended  by  the  adjustment  of  the  section  of  the  triangulation 
from  the  line  Sawnee  to  Gras.sy  to  the  line  Benn  to  King,  involving  the  solution  of  41 
equations,  and  finally  the  remaining  portion,  forming  a  central  figure  about  the  station 
Poore,  was  adjusted,  involving  the  .solution  of  13  equations,  including  a  length  equation 
introduced  for  the  purpose  of  bringing  the  lengths  derived  from  the  two  bases  into  accord. 

The  reasons  for  dispersing  the  small  outstanding  discrepancy  in  this  particular  figure 
are  given  in  the  portion  of  this  publication  which  treats  of  its  adjustment. 

The  fortunate  circumstance  that  the  Atlanta  and  the  Dauphin  Lsland  bases,  when 
connected  through  the  chain  of  intervening  triangles  or  more  complex  figures,  proved  to 
be  in  almost  exact  accord,  as  was  shown  by  the  .several  adjusted  pieces  of  triangulation 
gradualh'  joined  together  as  the  field  work  progre.s.sed ,  made  it  possible  to  retain  all  of 
these  five  partial  adju.stments.  This  carried  the  results  to  the  Dauphin  I.sland  base  net 
at  the  line  Spring  Hill  to  Daphne. 

It  was  thought  highly  desirable  to  extend  the  ol)lique  arc  as  far  as  the  city  of  New 
Orleans,  where  it  meets  with  and  terminates  at  a  well-determined  a.stronomic  .station. 
It  was  known  that  the  small  coast  triangulation  along  the  Gulf  from  Mobile  Bay  west- 
ward was  inferior  in  accurac>'  to  first-class  work.  Nevertheless  a  rediscu.ssion  and 
new  adjustment  showed  that  it  could  be  used  to  extend  the  arc  to  New  Orleans.  The 
whole  of  this  triangulation  is  old,  and  the  inferiority  of  the  work  is  due  to  the  difficulties 
encountered  on  account  of  the  climatic  conditions  along  the  Gulf  coast,  and  particularh^ 
to  the  effects  of  .severe  hurricanes  passing  across  this  region,  which  rendered  it  difficult 
to  preserve  the  stations  from  one  season  to  another.  It  was  also  most  important  to 
include  the  station  at  New  Orleans  in  the  discussion  of  the  local  deflections  of  the  plumb 
line  at  stations  approaching  and  in  clo.se  proximit>-  to  the  Gulf  of  Mexico. 


THE    MAIN   TRIANGULATIOX.  IO5 

B.  THE  TRIANGULATIOX. 

I.    NORTHKASTKRN    TKRMIXITS    TO    KPPING    BASK    XKT. 

The  extension  of  the  triangulation  from  the  primary  Hne  Cooper  to  Howard,  of  the 
Epping  base  net,  to  and  across  the  Canadian  boundary  at  the  St.  Croix  River  is  shown 
on  the  following  diagram.     The  geometric  figure  is  a  strong  one  and  demanded  for  its 

No.  16. 


167.  David 


Howard 


Kilometers 


10  20 

Statute  Miles 


adjustment  that  13  conditional  equations  l)e  satisfied.  Equal  unit  weights  were  given 
to  the  directions,  excepting  the  initial  line  Cooper  to  Howard,  to  which  a  double  weight 
was  assigned. 

The  angles  measured  with  the  repeating  circle  were  generall>'  made  up  of  jo  sets, 
each  of  three  repetitions  direct  and  three  repetitions  reversed  for  every  angle:  these 
results,  when  combinations  existed  among  the  measured  angles,  were  adjusted  at  each 


io6 


THE    EASTERN    OBLIQUE    ARC. 


station.      The  probable  error  of  an  observation  of  an  angle  (3  D.  and  5  2?.)  is  given  b\ 

e , 


and  that  of  a  direction  by  t\  =   e i    /^J2. 


The  approximate  elevations  of  the  stations  above  the  half-tide  level  of  the  Atlantic 
are  as  follows: 

Chanicook 

Trescott  Rock 

Prince  Regents  Redonbt     60 

Grand  Manaii 

Calais,  oVjservatory 

Howard 

Cooper 

No  reductions  to  the  horizontal  directions  for  heights  were  required. 


eters. 

Feet 

197 

647 

94 

3'o 

60 

197 

I  28 

420 

46 

150 

82 

269 

225 

738 

Abstracls  of  rt'siiltine:  horizontal  diit'ciioiis  obserz'cd  and   adjus/cd  at   stations  of  the  tria7igiitation 
extending  to  the  Canadian  boundary,  jS§g  to  /S6/. 


Hoivard, 
A.  D. 
have: 


Washington    County,   Maine.      July    and    August,    1S59.      75'='"  direction    theodolite    No.  i. 
Bache  and   G.  W.  Dean,  ob.servers.      P'roni  abstract  given  in  Part  I  of  this  publication  we 


No.  of 
directions. 


<  )bjects  observed. 


Resulting  directions 
from  .station  adjust- 
ment. 


Corrections 
from  pre- 
ceding fig- 
ure adjust- 
ment. 


Resulting 
directions. 


Corrections 
from  pre.s- 
ent  figure 

adjustment. 


Final 
seconds. 


Pigeon 
Cooper 

Trescott  Rock 
Grand  Manan 


o    CXI    00 '000       — o'oS9        00 '000 


108     01      27 '996  --0 '066 

173     43     51 '973  -0-026 

1S9     28     45  -843  -o  -026 

Mean  correction  — o  '026 


28-018  28-018 

52-036        -0-398         51  ■63S 
45-906        f  0-267         46-173 


Cot^/'c;',  Wa,shington  County,  Maine.  August  and  September,  1859.  75"^"'  direction  theodolite  No.  i. 
A.  D.  Bache  and  G.  W.  Dean,  observers.  25'"'  repeating  theodolite  No.  74.  October  23,  1867. 
C.  H.  Boyd,  observer. 


Chanicook 

Prince  Regents  Redoubt 

Grand  Manan 

Trescott  Rock 

Howard 

Mount  De.sert 

Rye  (Boyd)* 

Saint  David  (Boyd)* 


O  00  00  -QOO 

38  36  49  -082 

54  40  14  '493 

68  43  51  -687 

108  56  09  -385 

157  47  00  -789 

309  17  27-536 

329  01  51  -167 


-0  -068 

00  -000 

-1-0  -004 

00  -000 

-0  -068 

49  -082 

-0-951 

48-127 

—0  -068 

•4  -493 

+0  -646 

15  •"35 

-0-068 

51  -687 

-0  -058 

51  '625 

-0-226 

09  -227 

f  0  -415 

01  -272 

-0  -068 

27  -536 

—0  -802 

26  -730 

-0  -068 

51  -167 

+  1  -117 

52  -280 

Mean  correction  —  o  -068 
Probable  error  of  an  observation  (3  D.  and  3  j'?. )  of  a  direction,  <>, 


*  Number  of  sets  of  repetition  observations,  2. 


THK    MAIN    TRIANGULATION. 


107 


Abatracta  of  rcsultinfr  horizonlal  dirciiions  ohsicrvcd  and  adjusted  at  stations  of  the  tria7igiilation 
e.vtendint,''  to  the  Canadian  boundary,  /8^g  to  1861 — continued. 

Owwrof/',  New  Brunswick.     October  22  to  October  28,  1859.     75""  direction  theodolite  No.  i.     G.  W. 
Dean,  observer.      25""  repeatinj^  theodolite   No.  74.      C.  II.  Boyd,  observer,  1867. 


No.  of 
direction.s. 


16 


17 


IS 


19 


Objects  ob.served. 

Grand  Manan 

Prince  Regents  Redoubt 

Trescott  Rock 

Cooper 


--!i^!j^:;-\--'  frc^^l^S;,,. 


UJMS 

justinenl. 

0 

/ 

// 

// 

0 

00 

00  '000 

±0-139 

to  -491 

II 

23 

35  -285 
±0135 

-0150 

28 

'7 

21  '691 
±0-141 

— o-i6o 

88 

44 

50-139 

±0-173 

-0  -723 

"5 

16 

24  -874 

+0  -344 

138 

46 

22  -644 

+0-319 

165 

22 

52  -991 

—0-120 

20  .    Rye  (Boyd)* 

21  Calais,  observatory  (Boyd)* 

22  Saint  David  (Boyd)* 

Probable  error  of  an  observation  (3  D.  and  3  K.)  of  a  direction,  c,  = 
a  single  observation  of  a  direction,  e^  =  ±  i"  -08. 

Trescott    A'oc/c,  Washington  County,   Maine.     November    i    to   7,   1S61. 

No.  30.     C.  H.  Boyd,  observer. 


Final 
seconds. 

// 

CO 

000 

34 

-644 

21 

■040 

48 

•925 

24 

•727 

22 

■472 

52 

•380 

Probable  error  of 


30""  repeating  theodolite 


1 1 

Howard 

12 

Cooper 

13 

Chanicook 

14 

Prince  Regents  Redoubt 

15 

Grand  Manan 

0 

00 

CX3  -000 

+0-178 

oo-ooo 

74 

05 

21     565 

—0  -107 

21  -2S0 

124 

54 

05  -165 

-0-173 

04    814 

145 

27 

05  -458 

+0  -356 

05    637 

215 

10 

26  975 

-0  -253 

26  -544 

Number  of  sets  of  angles,  5;   probable  error  of  an  observation  (3  />.  and  3  R.)  of  a  direction, 


^,  =  ±  I 


Prince  Regents  Redoubt,  Washington  County,  Maine.     October  4  to  21,  1S61.     30"'"  repeating  theod- 
olite No.  30.     C.  H.  Boyd,  observer. 


23  Grand  Manan 

24  Trescott  Rock 

25  Cooper 

26  Chamcook 

Number  of  sets  of  observations,  7;  probable  error  of  an  observation  (3  Jh  and  3  A*.  1  of  a  direction. 
=  ±  I" -I. 


0 

00 

00  -000 

-0-371 

00  000 

60 

06 

1 2  -074 

— 0214 

12-231 

38 

37 

25  265 

+0-519 

26-155 

02 

39 

25  281 

+0-067 

25719 

*  Number  of  set.--  ot  repetitiou  observations,  3. 


io8 


THE   EASTERN    OBLIQUE   ARC. 


Ahslmcl^  of  irsul/iui;'  horiznntal  directions  observed  and  adjusted  at  stations  of  the  triangulation 
exte)idini^  to  tlie  Canadian  boundary,  iS§g  to  jS6i — continued. 

St.   David,  New  Brunswick.      September  30  to  October  2,    1867.      2^"''  repeatin.i^  theodolite  No.   74. 

C.  H.  Boyd,  observer. 


No.  of 
directions. 

Objects 

27 

Chanicook 

2S 

Calais,  observatory 

29 

Cooper 

3" 

Rye 

Results  from  station 
adjustment. 


O  00  00  '000 

67  I  r  50  -342 

72  23  49  -293 

S7  05  40  -032 


Corrections 
from  present  ad- 
justment. 


-OT53 

-0-319 

-o  '908 
-o  -436 


Final 
seconds. 


00  '000 
50-176 
50  '353 
39  749 


Number  of  sets  of  observations,  3;  probable  error  of  an  observation  (3  /?.  and  3  A'. )  of  a  <lirection, 

Rye,  Washington  Count)-,  Maine.      October  24-25,  1867.      25"^'"  repeating  theodolite  No.   74.      C.  H. 

Boyd,  observer. 


3" 

vSt.  David 

32 

Chanicook 

33 

Cooper 

9 

00 

00  '000 

—0-720 

00 -000 

42 

47 

52  -302 

+0-531 

53  '553 

45 

33 

44  -604 

+0-190 

45  '514 

Number  of  sets  of  observations,  2;  probable  error  of  an  observation  (3  D.  and  3  R. )  of  a  direction, 

Calais,  ob.servatory,   Washington  County,  Maine.      October   17-18,  1S67.      25'^"'  repeating  theodolite 

No.  74.     C.  H.  Boyd,  ob.server. 


34 

35 


St.  David 
Chanicook 


o    00     00  'ooo 
86     II     40  -903 


-0-319 
-0-319 


00  -000 
40  -265 


I 

Q: 

II 

Q: 

III 

Q: 

IV 

O: 

V 

O: 

VI 

0- 

VII 

o- 

^III 

0 

IX 

0 

X 

0 

XI 

0 

XII 

0 

SJIII 

0 

FIGURE   ADJUSTMKNT. 

Ohseri'ation  equations. 

=  +0-625-  (i)+  (2)-  (9)  +  (lO)-(ll)  +  (l2) 
=  ^2-090-  (7)+  (9)-(i2)-(-(i4)-(24)  +  (25) 
=  +0-691  (6)+  (9)-(i2)  +  (i3)-(i8)  +  (i9) 
=  +  1-981^  (6)+  (7)-(25)  +  (26)-(i7)  +  (i9) 
=  -i-,53i^  (4)+  (6)-(i9)  +  (2o)-(32)  +  (33) 
=  -1-485  -  (4)H  (5)-(29)  +  (3o)-(3i)+(33) 
=  -o-5o6-(2o)  +  (22)-{27)  +  (3o)-(3i)+(32) 
=  +  i-24i-(2i)+(24)-(27)  +  (28)-i34)  +  (35) 
=  +2  -18-0 -095(1)  + 1  -439(2)-!  •344(3)-o -249(10)4 

-o-454(i2)  +  i  -051(15) 
=  —0-70—1  -213(9)^  I  -295(8)  — 0-082(6)1  0-454(12) 

+0-625(18) -0-506(16) 
=  +4-31-1  -176(8)4  I  ■439(7)-o-263(6)-o-445(25)  +  i  -503(23) 

—  2  •io3(i6)  +  2 -150(17) 
=  +  i  -38-0 -254(  i5)+o-8i6(  i4)-o-562(i3)-o-i76(24)  +  i  -234(23)-!  -058  (26) -o -693  (  18) 

-2  •io3(i6)  +  2 -796(17) 
=  —2-60— 0-172(6)— o -415(4) +0-587(5)— 0-422  (19) +  0-598  (20)— 0-176  (22) +0-802  (29) 

—0-011(27)  -0-791(30) 


I  -544(9)-! -295(8)-o -597(11) 
~o-339(r5)-o-i!5(i3)-o-ii9(i9) 
I  -058(26)  —  0-047  (  19) 


THE    MAIN    TRIANGULATION. 


109 


It  -was  not  deemed  necessary  to  set  down  the  correlate  equations,  as  tliey  are  readily 
formed.     The  directions  (i)  and  (10)  each  have  the  weight  2. 


Normal  equations. 


C„ 


C.3 


0= 

4-0  -625 

0= 

—  2  -090 

0= 

+  0-691 

0= 

+  I-981 

0= 

-1-531 

0= 

-1-485 

0= 

—0  -506 

0= 

+  1  -241 

0= 

+  2-18 

0  = 

—  0  -70 

0= 

f4'3i 

0= 

+  1-38 

0= 

—  2  -60 

+  5 


-2  —  2 
-6+2  —2 

+6  +2  -2 

+  6  —2 

+6 


+2  —2 

+6  +2 

+6  +2 
+6 


-0  -039 

+  1-667 

+1  -998 

- 1  -667 

—   I  -884 

-r  0-992 

+1-998 

-2-444 

"i    0-216 

+  0-131 

-0-250 

-0  -037 

—    I  -108 

-  3  -854 

—0  -250 

+0  -037 

—  0-216 

+  1-263 
-0-591 
-I  -554 

+9  -6407 

-4-1123 

+   I  -5229 

—  0  -2670 

—0-165 

+4-1502 

-  0-4316 

-r  0-7817 

—0  -0643 

+  16  -1466 

-13  -4081 
+  16-4398 

^00651 

Resulting  correlates : 


C,=  —0-044  62 

C8=    -0-318    64 

C,=  +0-I75  49 

C  9=  —0-222  77 

€3=  —0  -06  r  44 

C,r,=  -0-109  49 

C4=    -0-152    S3 

C„=  -^0-428  84 

Cs=  -0-074  77 

C„=  +0-221  47 

C6=    +0  -264    38 

C„=  +1  -462  42 

C,=  +0-456  00 

-2  -3S20 


and  the  resulting  corrections  to  directions: 


(l)* 

=  +  0-0329 

(  8) 

=  +0-6510 

(15)  = 

=  -0  -2534 

(22)  = 

—0-1200 

(29)  = 

-0-90S4 

(2) 

-0  -3652 

(  9) 

-0  -0525 

(16) 

-+ 0-4913 

(23) 

—0-3712 

(30) 

-0  -4364 

(3) 

+0  -2994 

(io)-» 

■      +0  -0054 

(17) 

-0-1498 

(24) 

-0-2I45 

(31) 

-0  -7204 

(4) 

-0  -7965 

(II) 

+0-1776 

(18) 

—0  -1605 

(25) 

-0-5191 

(32) 

-0  -5308 

(5) 

+  1  -1228 

(12) 

—0  -1072 

(19) 

-0  -7233 

(26) 

+0  -0666 

(33) 

-r-0-1896 

(6) 

+0  -0097 

(13) 

-0-1733 

(20) 

+0  -3437 

(27) 

-0-1535 

(34) 

—0-3 1 86 

(7) 

-0  -9453 

(14) 

+0  -3562 

(21) 

+0  -3 1 86 

(28) 

—0-3186 

(35) 

—0-3186 

Probable  error 

of  an 

observed  direction,  0  674  _l          = 
V    13 

±o"-5i 

♦Directions  (i)  and  (lo)  were  given  double  weight  in  the  adjustment. 


no 


THE    EASTEHN    OBLIQUE    ARC. 


Resulting  angles  and  sides  of  the  triangulation  between  the  Epping  base  net  and  the  northeastern 

terminus  of  the  are. 


No. 


Stations. 


Obsen-ed  ans;les. 


Correc- 
tion. 


Spher- 
ical 
angles. 


Spher- 
ical 
excess. 


Log.  dis- 
tances. 


Distances  in 
meters. 


7  { 


Trescott  Rock 

Howard 

Cooper 

Grand  Maiiaii 

Howard 

Cooper 

Grand  Manan 
Howard 
Trescott  Rock 

Grand  Manan 
Trescott  Rock 
Cooper 

Prince  Regents  Re 

doubt 
Grand  Manan 
Trescott  Rock 


74  05  21  -565 

65  42  24"oiS 

40  12  17-540 

44  16  

Si  27  17  -888 

54  15  54  734 

19  25  

15  44  53  ■•'^70 

144  49  33  '025 

24  51  

141  05  05  '410 

14  03  37  '194 


60  06 
50  10 
69    43 


Prince  Regents  Re- 
doubt 1 38 
Grand  Manan  25 
Cooper  16 

Chanicook 
Grand  Manan 
Cooper 

Chamcook 
Grand  Manan 
Trescott  Rock 


03 


44 
34 
40 

n 
26 

[6 


Chanicook 
Trescott  Rock 
Cooper 

Chanicook  1 1 

Grand  Manan  1 1 

Prince  Regents  Re- 
doubt 157 


12-074 


21  -517 


Prince  Regents  Re- 
doubt                      78  31  13-191 
Trescott  Rock          71  21  43  -893 
Cooper                        30  (17  02  -605 


37  25  -265 

■9  

25-411 


8S 
36 
54 

28 

61 
90 

60  27  2S  -448 
50  48  43  -600 
68  43  51  -687 

II  23  35-285 
•I      15      


50-139 

14  '493 
21  -691 

21  -810 


-0-285 
-o  -398 
+0  -05S 


20    34-719 


+0-267 
— o  -646 


+0  -664 
+0-431 


— o  -146 
-o  -704 

+0-157 


— o  -6in 

+0  -734 
+0  -463 
+0  -893 

+  0  -890 


-I  -596 

-I  -215 


+0  -641 
-0-652 


-o  -080 

-o  -563 
-o  -066 
-o  -062 

-o  -642 


21  -280 
23  -620 

i7'59« 

52-451 
1S-155 
54  -088 

32  -875 
54  '534 

33  '456 

19 '577 
05  -264 
36  -490 

12-231 

27  -8S0 

20  -907 

13  '925 
44  ■?>S(> 
03  -49S 

26-155 
08  -304 
27  -007 

48  -924 
59  "925 
15  "134 

21  '039 
19-501 
21  -730 

27  '885 
43  '534 
5'  '625 

34  '643 
51  -622 


0-832 
0-833 
0-833 

I  "565 
I  '564 
I  '565 

0-288 
0-288 
o  -289 

0-444 
0-443 
o  -444 

0-339 
0-339 
0-340 

0-593 
0-593 
0-593 

o  -488 
o  -4S9 

0  -489 

1  '327 
I  -328 
I  -328 

0-757 
0-757 

0  756 

1  -015 
I  -015 
I  -014 

o  -182 
o  -182 


4  -603  402  I 
4  -580  099  7 
4-430  277  o 

4  -603  402  I 
4-754  589  2 
4  -668  845  2 

4-430  277  o 
4-342  006  7 
4  -668  845  2 

4  -580  099  7 

4  754  5S9  I 
4-342  006  7 

4  -342  006  7 
4  -289  384  2 
4  '376  239  o 

4  -5S0  099  7 
4-565  481  2 
4-289  384  2 


-0-438        34-281         0-182 


4  754 
4-565 
4  -376 

4-754 
4-529 
4-666 

4-  342 
4-609 
4-666 

4-580 

4-529 
4-609 

4-376 
4-371 


589  2 
481  2 
239  2 

589  2 
929  o 
298  r 

006  7 
948  2 
298  o 

099  7 
929  I 
948  2 

239  I 

372  7 


40  123-81 
38  027  -67 
26  932  -52 

40  123  'Si 

56  S31  -51 
46  649-31 

26  932  -52 
21  978-94 
46  649  -3 1 

38  027  -67 
56  831  -50 
21  978-94 

21  978-94 
19  470  -82 
23  781  -49 

38  027  -67 
36  768  -95 
19  470  -82 

56  831  -51 
36  76S-95 
23  781  -50 

56  831  -51 
33  878  -88 
46  376-51 

21  978-94 
40  733 -f7 
46  376-50 

38  027  -67 
33  878  -88 
40  733-17 

23  781  -49 
23  516-50 


4  -666  29S  o    46  376  50 


THE    MAIN    TRIANGULATION. 


Ill 


Rcsul/inff  ans^lcs  and  sides  of  llu 


lrianv;nlalion  hctivecn  the  lippinu;  base 
lenitinits  of  the  arc — continued. 


net  and  the  northeastern 


No. 


i.^ 


14 


[5 


16 


17 


iS 


Stations. 

Ohservei 

1  anjjlfs. 

Correc- 
tion. 

ical 
angles. 

ical 
excess. 

I^og.  dis- 
tances. 

UisUinces  in 
meters. 

0 

/ 

// 

// 

// 

// 

Clmnicook 

16 

5.^ 

46  '406 

—0  -oil 

46  '395 

0  -235 

4  -2«9  384  2 

19  470-82 

Prince  Regent.s  Re 

doubt 

142 

33 

13  -207 

+  0-281 

13-488 

0. 236 

4  -609  948   2 

40  7,33-17 

Trescott  Rock 

20 

33 

00  -293 

+  o-53fJ 

00  -823 

0  -235 

4-371 

372  7 

23  516-50 

Chamcook 

77 

2r 

'4  -854 

-0-574 

14  -280 

0-657 

4-565    481     2 

36  768  95 

Prince  Regents  Re- 

doubt 

64 

01 

60  '016 

-0  -452 

59  '564 

0  -657 

4  -529  929   ' 

33  878  -88 

Cooper 

3« 

36 

49  '082 

-0  '955 

48-127 

0-657 

4-37' 

372  8 

23  516-51 

Rye 

102 

45 

52  -302 

-0  -342 

51  -960 

0  -344 

4  -529 

929   I 

33  878  -88 

Chamcook 

26 

3' 

34  "735 

+ 1  -067 

35  '802 

0  -344 

4  ■I9<^' 

727  0 

15  514-11 

Cooper 

50 

42 

32  -464 

+0  -806 

33  '270 

0-344 

4-429 

504  7 

26  884  -67 

vSt.  David 

72 

23 

49  '293 

i-i  -061 

50  -354 

0-510 

4-529 

929  I 

33  S78  -8S 

Chamcook 

76 

3''^ 

02  -852 

+0  -603 

03  -455 

0-509 

4  -538 

830  5 

34  5S0  -44 

Cooper 

3" 

58 

08  -833 

-1-113 

07  -720 

0  -510 

4  -262 

199  9 

18  289  -42 

St.  David 

87 

05 

40  -032 

-0  -283 

39  749 

0-319 

4-429 

504  7 

26  8S4  -67 

Chamcook 

50 

06 

28-117 

-0  -463 

27  -654 

0-319 

4-315 

000  5 

20    653  -.S2 

Rye 

42 

47 

52  -302 

+  1  -252 

53  '554 

0-319 

4  262 

200  0 

18    289  -42 

St.  David 

14 

41 

50  739 

- 1  -345 

49  '394 

0-153 

4-190 

727  0 

15    5I4-II 

Cooper     '' 

19 

44 

23-631 

+  1  -920 

25-55' 

0-153 

r3>5 

000  4 

20    653  -82 

Rye 

145 

33 

44  -604 

+0-910 

45-514 

0-153 

4  -538 

830  5 

34  580  -44 

Calais  Observatory 

86 

11 

40  -903 

-0  -637 

40  -266 

o-|  17 

4-262 

200  0 

iS  2S9  -42 

St.  David 

67 

1 1 

50  -342 

-0-165 

50-177 

0  - 1 1 7 

4-227 

816  4 

16  S97  26 

Chamcook 

26 

36 

30  -347 

-0  -439 

29  -908 

0-117 

3  -914 

328  3 

8  209  -72 

2.    EPPING     BASE    NET     TO     MASSACHUSETTS    BASE    AND    TO     FIRK    ISLAND     BASE     NET, 
MAINE,    NEW    HAMPSHIRE,    MASSACHUSETTS,     RHODE    ISLAND,   AND   CONNECTICUT. 
•      1844-1882. 

The  main  triaiigulation  which  connects  and  is  based  upon  the  three  northern  base 
lines  is  among  the  most  elaborate  pieces  of  field  work  ever  executed  b\-  the  Stirve\-.  It 
was  steadil}'  contintted  and  completed  by  Superintendent  Bache  and  his  party  in  twenty 
years.  Only  one  station  (Mount  Washington)  was  afterwards  included  in  the  scheme. 
There  are  also  several  subordinate  stations,  not  referred  to  here,  which,  in  addition  to 
what  is  furnished  by  the  principal  stations,  effects  the  junction  with  the  subordinate, 
secondary,  and  tertiary  work  covering  the  greater  part  of  the  coast  line  of  Massachusetts, 
New  Hampshire,  ard  Maine. 

With  the  exception  of  the  angles  at  the  Massachusetts  base,  all  angular  directions 
were  measured  by  means  of  the  great  (so  called)  75""  theodolite,  and  the  station 
results  were  deduced  by  application  of  Bessel's  least  .square  method  of  reduction.  The 
accuracy  reached  is  quite  commensurate  with  the  amount  of  labor  spent,  both  in   the 


112 


THE    EASTERN    OBLIQUE    ARC. 


Hximpbojck}. 


THE    MAIN    TRIANGULATION. 


113 


field  and  in  the  office.  This  may  l)e  seen  in  the  closing  errors  of  the  52  trianj^les  as 
well  as  in  the  numerical  constants  of  the  57  conditicMial  equations.  The  first  adjustment 
of  this  triangulation,  made  in  1866  under  the  writer's  direction,  avoided  the  heavy  work 
of  .solving  simultaneously  this  large  number  of  equations  by  dividing  the  whole  work 
into  three  parts,  but  in  this  di.scu.ssion  it  was  decided  to  treat  the  adjustment  rigorously 
as  a  whole.  The  new  results,  however,  differ  but  slightly  from  the  older  ones.  The 
directions  in  the  new  adjustment  are  corrected  f(jr  effect  of  altitude  of  the  stations 
sighted,  and  the  observations  made  at  and  upon  Mount  Wa.shington  are  now  incorporated 
into  the  general  scheme. 

Approximate  heights  0/  stations  alwve  the  average  level  of  the  Atlantic  Ocean. 


Mtters. 

Hect. 

Meters. 

Feel. 

Humpback 

451 

I    480 

Manomet 

120 

394 

Mount  De.ser*. 

465 

■    525 

Blue  Hill 

'94 

635 

Mount  Harris 

3^^^ 

I    251 

Beaconpole 

167 

54'S 

Ragged  Mountain 

397 

I    301 

Monadnock 

966 

3  1 68 

vSabattus 

244 

Soo 

Wachusett 

616 

2  022 

Mount  Bhie 

976 

3  202 

Mount  Tom 

372 

I  220 

Mount  Pleasant 

615 

2  018 

Bald  Hill  (Tolland  County) 

393 

I  290 

Mount  Wasliington 

I  920 

6  300 

Box  Hill 

259 

850 

Mount  Independence 

153 

501 

Ivy 

498 

I  634 

Gunstock 

732 

2  402 

Sandford 

273 

S95 

Aganienticus 

222 

72S 

Wooster 

305 

I  000 

Unkonoonuc 

411 

>  34S 

Copecut 

108 

353 

Thompson 

S3 

271 

Great  INIeadovv 

81 

265 

Ob.servation  eqitation  LVI  is  the  length  equation  between  the  Epping  base  (referred 
to  the  line  Humpback  to  Mount  Desert)  and  the  Massachusetts  ba.se,  .showing a  di.screp- 
ancy  of  but  57  units  in  the  .seventh  place  of  decimals  in  the  logarithms,  and  the  corre- 
.sponding  equation  No.  LVI  I  is  the  length  equation  between  the  Massachusetts  base  and 
the  Fire  Island  base  ( referred  to  the  line  Sandford  to  Wooster )  and  shows  a  discrepancy 
of  but  26  units.  Weights  to  the  131  directions  are  introduced  on  the  same  principle  as 
was  done  in  1866,  which  takes  care  of  the  circumstance  that  the  relative  weights,  when 
the  directions  are  combined  to  form  triangles,  are  very  diiiferent  from  and  only  partly 
resemble  the  weights  deduced  from  the  station  adjustment  alone.  Experience  ha.s 
shown  that  the  former  are  at  least  of  equal  if  not  greater  importance  than  the  latter. 

The  maxinuim  clo.sing  error  in  the  .sum  of  the  angles  of  any  one  triangle  is  but  2""o 
and  the  average  closing  error  of  a  triangle,  found  by  ,s(|uaring  the  52  errors,  is  given 

by  ^^^-^ 


52 


dro"'92;   hence  the  probable  error  of  a  direction   i.s  0*674 -_": 

V6 


:±0       2^  = 


On   the  other   hand   the   approximate  proliable  error  of  a  direction   derived  from  the 


stalioii  adjustment  alone"'- is  foiuul  from   the  average  .sqtutre 


3 '05^^ 


VIZ. 


■,  =  Vo-0233  = 


=bo"i53;    hence   the  .square  of    the   combination  error  or  «'/ =  (o"255)=— (0153)== 
(o'204)\     To  each  of  the  values  of  <\',  therefore,  was  added  (o'204V'  or  0*040  in  order 


*See  re.suUiiig  probable  errors  of  tlie  direction  presented  lurtlier  on  with  the  abstraetsof  the  horizontal  measures 

4192 — No.  7 — 02 S 


114 


THE    EASTERN    OBLIQUE    ARC. 


to  get  E"  =  -,  but  in  order  to  make  the  average  value  of  the  131  cases  equal  to  uuity 

this  was  multiplied  by  1575;  hence  the  final  reciprocals  of  weights  used  in  the  adjust- 
ment further  on. 

Abstrac/s  of  horizontal  direcfions  as  observed  and  adjusted  at  the  principal  stations  betiveen  the  Epping 
base  net,  the  Massachusetts  base,  and  the  Fire  Island  base  net,  184-^-/882. 


Humpback,  Hancock  County,  Maine.     Juh-  ig  to  September  6,  185S.     75' 

A.  D.  Bache  and  G.  W.  Dean,  olxservers. 


direction  theodolite  No.  i. 


Number 
of  direc- 
tions. 

objects  obser\ 

'ed. 

Resulting  di- 
rections from 
station  ad- 
justment. 

Approxi- 
mate 
probable 
errors. 

Correc- 
tions 
from  net 
adjust- 
ment. 

Correct- 
ed direc- 
tions. 

Reduc- 
tions to 
sea  level. 

Result- 
ing .sec- 
onds. 

Cooper 

0 
u 

00 

00  'OOO 

±0-15 

—0-196 

00 -000 

00 '00 

Azimuth  Mark 

39 

37 

40-230 

0  -16 

—0-023 

40  -403 

Mount  Desert 

114 

33 

50 -877 

0  -09 

+0-583 

51  656 

+0  -008 

51-66 

3 

Ragged  Mountain 

154 

28 

20  -545 

0-13 

—  0  -023 

20-718 

4-0-022 

20-74 

Saunders 

165 

12 

47-118 

0-13 

—0-023 

47  -291 

4 

Mount  Harris 

I  So 

36 

29-988            0*17 
Mean  correctio 

—0  -023 

30-161 

-Ho -010 

30 '17 

n     -0-023 

Correc- 
tions 
from 
figure 
adjust- 
ment. 


-1-0 -36 


Final 
seconds. 


2973 


Circle  used  in  V  positions. 


Mouiit  Desert,  Hancock  County,  Maine.     August   14  to  October  14,  1S56.     75' 
No.  I.     A.  D.  Bache  and  G.  W.  Dean,  observers. 


direction  theodolite 


Isle  au  Hant 

0 

00 

00  "ooo 

±o'i4 

—0  -006 

00  "000 

00  -00 

Ragged  Mountain 

33 

39 

21  -332 

o-ii 

—0  -006 

21  332 

-1-0  -009 

21-34 

—  0  -05 

21  '29 

Mount  Harris 

70 

54 

51 '93' 

0-12 

—  o*oo5 

51 -931 

—0-017 

51  -91 

-ho-io 

52    01 

Saunders 

93 

48 

58 -.■^82 

0  *IO 

—  o"oo6 

58  -382 

Azimuth  Mark 

122 

49 

25 '136 

0  *10 

—  0  -  006 

25-136 

Humpback 

144 

20 

00  -152 
Mean 

0  '10 

correction 

-0-143 

00-015 

4-0 -ooS 

00-02 

—  0  006 

Circle  used  in  "V  positions. 

Dlount  Harris,   Penobscot  County 
No.  I. 


nner  or 
ctions. 

objects  Qbser\'ed. 

Thomas  Hill,  Ban- 

gor 

Azimuth  Mark 

Peaked  Mountain 

5 

Humpback 

Saunders 

6 

Mount  Desert 

I.sle  au  Haut 

7 

Ragged  Mountain 

« 

Sabattus 

9 

Mount  Blue 

Circle 

used  \w  V  positions 

,  Maine.     Jvilj'  25  to  October  17,  1855.     75 '^"' direction  theodolite 
A.  D.  Bacjie  and  G.  W.  Dean,  observers. 


Resulting  direc- 
tions from 
station  adjust- 
ment. 


nta'te't'?mb     Reductions     Resulting 
ableer'^ot   to  sea  level.      seconds. 


0  00  00 -000      zbOTI 

1  16  32-750  0'12 

9  50  32  -207 

13  14  12-055 

29  29  47  -495 

53  46  37-3'2 

85  58  21-672 

118  55  14-559 

170  57  33  -572 

213  17  48  -992 


Corrections 

from 
figure  ad- 
justment. 


Final 
seconds. 


0-13 

Q-og 

+0-013 

12  -07 

—0  -QI 

12  -06 

Q-og 

0  'og 

—  0  -020 

37-29 

+0-07 

37  -36 

Q-II 

0  -IT 

0  "GOO 

14-56 

+o-o6 

14  -62 

0  -12 

+0-013 

33-58 

— c  -01 

33-57 

0-13 

—0  "009 

48-98 

— o"ii 

48-87 

i 


THE    MAIN    TRIANGULATION. 


II 


Abstracts  of  horizontat  directions  as  observed  and  adjusted  at  the  princ:pat  stations  l^tween  the  Eppin^ 
base  net,  the  Massachusetts  base,  and  the  Fire  Island  t>ase  net,  /^^.^-/^^.-cont.nued.        • 

J?a^^ed  Mountain,  Waldo  County,  Maine.    AukusI  9  to  November  2 . ,  .854.    75 ' "'  'Predion  theodolite 
No.  I.     A.  D.  Bache  and  G.  W.  Dean,  oljservers. 


Number  of 
directions. 


Objects  observed. 


Resulting  direc- 
tions from 


Reductions     Kesultinf; 


Itingdirec-  Annroxi- 

itis  from  Approxi       deductions      Kesumn 

station  acSjust-  ,"^tfe?rot:  to  sea  level.       seconds 
ment. 


Corrections 

from 
figure  ad- 
justment. 


Final 
seconds. 


// 


Cape  Small 
Mount  Pleasant 
Sabattus 
Mount  Blue 
Mount  Harris 
Azimuth  Mark 
Saunders 
Humpback 
Mount  Desert 
Isle  au  Haut 
Circle  used  in  V  positions. 


O  00  fK)  'OOO 

32  27  39  '339 

35  05  22  -195 

72  13  02  -447 

130  54  59  '344 

131  32  49 '928 
171  43  10-933 
179  05  58-  378 
20S  3 1  00  -500 
241  oS  17  -507 


// 
d=o-i3 
0-19 
o'i7 

OT2 
OM  I 
0'l6 
O  '12 

o-i8 

O'll 

o  '19 


// 


// 

00  TJO 


+0-0I0 

39 '35 

-o'39 

39  74 

+0  -003 

22  '20 

-0-27 

21  -93 

—0  -049 

02  -40 

-4-0  -I  I 

02  -5 1 

0  -ooo 

59  '34 

—0  -20 

59"'4 

+0  -025 

58  -4" 

Q-OO 

58-40 

+0-OII 

00-51 

+0-04 

00-55 

Afount  Blue,  Franklin  County,  Maine.     August  29  to  November  5,  1S53.     75  ^  airection  theodolite 
No.  I.     A.  D.  Bache  and  G.  W.  Dean,  observers. 


Peaked  Mountain 

0 

00 

00  -ooo 

±0-14 

00  -00 

Saunders 

7 

35 

33  784 

0-17 

16 

Mount  Harris 

8 

46 

42  -896 

o-iS 

—0-003 

42-89 

-024 

42-65 

17 

Ragged  Mountain 

35 

42 

23  70S 

0-16 

—  0-019 

23 '69 

4-0-15 

23 '84 

Cape  Small 

74 

II 

02  -283 

0-20 

18 

Sabattus 

76 

57 

34  '640 

0-15 

— o-oo8 

34-63 

+0-15 

3478 

19 

Mount  Independence 

94 

02 

02  -93S 

0-30 

0  -000 

02-94 

—0  -20 

02-74 

20 

Mount  Pleasant 

121 

17 

49-712 

0-15 

+0  -027 

49  74 

+0-03 

49  77 

Circle  used  in  IV  positions. 

Sabattu^,  Androscoggin  County.  Maine.     June  18  to  Attgust  16,  1853.     75  ^■"  clirection  theodolite 
A.  D.  Bache,  C.  O.  Boutelle,  J.  E.  Hilgard,  and  G.  \V.  Dean,  observers. 


23 

24 
25 

21 
22 


Mount  Blue 
Azimuth  Mark 
Mount  Harris 
Ragged  Mountain 
Cape  Small 
Mount  Independence 
Mount  Pleasant 


o  00  00  -000 

17  56  05  -204 

69  29  07  -402 

loi  37  20  -637 

172  59  00-194 

222  21  04-15S 

275  46  51  '399 


±0  -II 
o  -17 
o  -18 
0-17 
o  -14 

0-13 
0-14 


-o  -032 


59-97 


-+-0  -021 

+0  -005 


07-42 

20  -64 


4-0-007 

^  o  -1)14 


04-16 

51  -41 


— 021 

4-o-i6 
-f  0-24 

— o  -07 
— o  -02 


No.  I. 


59-76 


07-58 

20 -ss 


04-09 
51  -39 


N.  B.     The  observation  of  the  direction  to  Mount  Washington  is  too  weak  to  be  admissible. 
Circle  used  in  IV  positions. 


ii6 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directions  as  observed  and  adjusted  at  the  principal  stations  between  the  Epping 
base  net,  the  Massachusetts  base,  and  the  Fire  Island  base  net,  /84^f-7882--continued. 

Mount  Pleasant,  Oxford  Comity,  Maine.     July  2  to  August  16,  1851.     75 "^"^  direction  theodolite  No.  i. 
A.  D.  Baclie,  W.  P.  Trowbridge,  and  G.  W.  Dean,  observers. 


Number  of 
directions. 

Objects  observed. 

Resulting  direc- 
tions from 
station  adjust- 
ment. 

Approxi- 
mate prob- 
able errors. 

Reductions 
to  sea  level. 

Resulting 
seconds. 

Corrections 
from 
figure  ad- 
justment. 

Final 
seconds. 

0 

/ 

// 

// 

// 

// 

// 

// 

26 

Mount  Blue* 

0 

00 

GO  '000 

drO-IO 

+0  -043 

00 -04 

—  G  -II 

59~'93 

27 

Sabattus 

51 

26 

46  -938 

0  '12 

-f  0  -006 

46-94 

+  0-13 

47  '07 

28 

Ragged  Mountain 

54 

39 

35  737 

0'14 

+0  -007 

35  74 

—  0  -20 

35 '54 

Cape  vSmall 

S3 

01 

37  -055 

G  -11 

29 

Mount  Independence  100 

12 

48  -045 

0-09 

—0  'ooS 

48  -04 

-0-49 

47  '55 

Ossipee 

146 

17 

24  '539 

o-o8 

30 

Againenticiis 

147 

14 

47  -657 

G  -14 

— G  -003 

47 '65 

+  0-77 

48 -42 

31 

Gunstock 

192 

06 

52  -382 

0  '09 

+  0  '040 

52-42 

-G-23 

52-19 

34 

Mount  Washington 

279 

18 

34-810 

G  -24 

—  G  '102 

3471 

+0-38 

35-09 

Circle  u.sed  in  V  positions. 

Mount  Independence,  Cumberland  County,  Maine.     September  2  to  October  19,  1849.     75""  direction 
theodolite  No.  i.     A.  D.  Bache  and  G.  W.  Dean,  observers. 


39  Mount  Blue  g     00  00  -ooo 

44  36  -450 

4G  Sabattus  25     16  42-166 

33  03  -048 

51  14 '438 

49  46  -990 

37  Gunstock  253     42  01  -296 

28  23  -886 

N.  B. — Observation  of  direction  to  Mount  Washington  too  rough  for  use. 
Circle  used  in  VI  positions. 

Mount  Washington, ■\  Coos  County,  Ne-w  Hampshire.     Station  mark  of  1851  and  i860.     30^"'  direction 

theodolite  No.  118.     July  31  to  September  13,  1882.     J.  A.  McNicol,  observer  (R.  D.  Cutts,  chief 

of  party). 

^-^'  ^        ,  1 1  It  It  It  1 1  t  f 


Mount  Blue 

G 

Azimuth  Mark 

0 

Sabattus 

25 

Cape  Small 

>      87 

Agamenticus 

207 

Ossipee 

241 

Gunstock 

253 

Mount  Pleasant 

307 

±G-I4 

—  0  -002 

OG  -GO 

+0-36 

00 

36 

0  -16 

0  15 

-fo  -QIC 

42  -18 

-|-o  -02 

42 

20 

0  -16 

G-I7 

-f  G  -010 

14-45 

— 0-3G 

14 

■15 

0  -20 

0  -20 

+  0  -023 

01  -32 

—0-60 

00 

-72 

0-13 

-G  -G33 

23-S5 

+0-29 

24 

-14 

Reference  Mark 

G 

OG 

GO  -GO 

±0-07 

33 

Mount  Blue 

46 

31 

41  -34 

0  -II 

+  G  -02 

41  -36 

-G-I3 

41  -23 

34 

Mount  Pleasant 

115 

27 

23  -90 

G-13 

—  0-03 

23-87 

—0  -16 

23-71 

35 

Gunstock 

174 

08 

45-65 

0  -14 

O-QO 

45-65 

-fO-30 

45-95 

Killington 

229 

44 

57-67 

G-I7 

Mount  Mansfield 

274 

iS 

19  -g8 

0-I4 

Circle  u.sed  in  VII  positions. 

*  .\7.imuth  mark  west  of  Mount  Blue  2"-i9  ±  o"-ii. 

tThis  station  was  established  in  September,  1849,  by  T.  McDonnell  at  the  highest  part  of  the  mountain.  It  was 
marked  by  a  copper  bolt  inserted  in  a  bowlder  by  G.  A.  Fairfield  in  1851,  and  re-marked  in  1853  by  B.  F.  West.  The  pole 
placed  over  the  mark  was  observed  upon  from  Mount  Independence  in  1849,  from  Ossipee  in  1851,  and  from  Sabattus  in 
1853,  but  only  roughly.  The  observations  from  Mount  Pleasant  in  1851  and  from  Gunstock  in  i860,  however,  were  quite 
satisfactory.  In  1877  C.  H.  Sinclair  vLsited  the  station  and  under  the  direction  of  Assistant  R.  D.  Cutts  connected 
geodetically  the  several  eccentric  station  marks  since  1873  and  again,  in  iSSo  and  1881,  those  used  by  Prof.  E.  T.  Quimby 
in  his  survey  of  the  State  of  New  Hampshire.  These  last  obser\'ations  have  no  bearing  on  the  oblique  arc,  the  only 
direction  in  common  being  that  to  Sabattus.  Between  July  31  and  September  13,  1.S82,  Assistant  Cutts  and  Aid  J.  A. 
McNicol  observed  horizontal  angles  at  the  station  in  connection  with  the  survey  of  New  Hampshire,  b\it  included  the 
three  directions  to  Mount  Blue,  Gunstock.  and  Mount  Pleasant.     The  30':")  theodolite  was  then  employed. 


THE    MAIN    TRIANGULATION. 


117 


Abstracts  of  horizonlal  directions  as  ol>scri>e(l  and  adjusted  at  tlic principat  stations  between  the  I-,ppinjr 
base  net,  the  Massachusetts  base,  and  the  Fire  /stand  ttase  net,  /<?//-/AV^— continued. 

AganienticHS,  York  County,  Maint.     Auj^ust  30  to  October  10,  1S47.     75' 

A.  D.  Bache,  observer. 


direction  theodolite  No.   I 


Number  of 
direction.s. 


Objects  ob.served. 


ResultiiiK  direc- 
tions from 
station  adjust- 
ment. 


Approxi- 
mate prob- 
able errors. 


Keduc'ions     ResuUinx 
to  sea  level.      seconds. 


Corrections 
•  from 
figure  ad- 
justment. 


Final 
seconds. 


Isle  of  vShoals                  o  00  cvj '000  ±o-i5 

49  Thompson                        i6  20  22-029  o'i4 
Holt                                  41  28  13 '964  0-17 

50  Unkonoonuc                   83  56  21-852  0-17 
Patuccawa                       88  19  23-555  o -16 

51  Gunstock                       134  44  12-364  0-13 

52  Mount  Pleasant           187  02  56-311  0.14 
Ossipee                           188  12  18-168  o-r4 

53  Mount  Independence  220  23  53-621  0-14 
Azimuth  Ma-k             307  52  25-880  0-17 

Circle  used  in  V  positions. 

GunstocI;,*  Belknap  County,  New  Hampshire,  July  ii   to  August   15,  i860 

No.  1.     G.  W.  Dean,  observer. 


0  -000 

22-03 

^0-39 

22    42 

0-015 

21   -87 

-0  -32 

21  -55 

0-037 

12-33 

-l-o.  02 

12-35 

0-008 

56-30 

—0  -16 

56 -'4 

0  -007 

53  -63 

—  0  "OI 

53  64 

75' 


direction   theodolite 


Azimuth  Mark 

0 

00 

00  -QOO 

±0-14 

00  -00 

41 

Mount  Washington 

44 

06 

20  -238 

0  -u 

+  0-014 

20  -25 

—0  -40 

19  -^5 

42 

Mount  Pleasant 

7« 

13 

23  -269 

0  -u 

-f  0-034 

23-30 

— 0  -04 

23-26 

43 

Mount  Independence  1 12 

33 

03-490 

o-ii 

-f  0  -005 

03  -50 

—  0  -So 

04-30 

Ossipee 

121 

29 

34-600 

0  -12 

44 

Agamenticus 

161 

02 

47  -320 

0  -12 

— o-oii 

47-31 

— 0  -08 

47-23 

45 

Thompson 

192 

55 

14  -997 

0.  12 

— 0  -004 

14-99 

—0  -20 

14-79 

Patuccawa 

202 

52 

41  -124 

0  -II 

46 

Unkonoonuc 

237 

14 

12-358 

0-08 

+0  -013 

12-37 

— o-io 

12-47 

47 

-Wachusett 

240 

56 

10  -060 

0  -09 

+0  -023 

10  -oS 

—0  -40 

09  68 

48 

Monad  nock 

260 

13 

18-732 

0  -07 

-1 0  -054 

18  -79 

-0-15 

18  -94 

Circle  used  in  -V  positions. 

Unkonoonuc,\  Hillsboro  County,  New  Hampshire.  August  29  to  October  6,  1S48.  75""  direction 
theodolite  No.  i.  A.  D.  Bache,  observer.  August  25  to  29,  i860.  G.  \\'.  Dean,  observer.  Same 
instrument. 


Gunstock 

0 

00 

00  -000 

±0  -07 

+0  -023 

00  -02 

+001 

00  03 

59 

Patuccawa 

47 

43 

13  -998 

0-I2 

Agamenticus 

53 

00 

53-613 

0-13 

-(-0  -008 

53- 62 

—0  -II 

53  '73 

54 

Thompson 

103 

24 

13  952 

0  -09 

—0  -004 

13- 95 

+0  -02 

13-97 

55 

Holt  and  Azimuth 

Mark 

117 

12 

51  -745 

0    II 

56 

Blue  Hill 

138 

49 

1 1  "993 

0-I5 

—0  -009 

11  -98 

-0  -35 

1 1  -63 

57 

Wachusett 

187 

30 

54-272 

0  -07 

40  -027 

54  "3" 

-  0-16 

54-46 

58 

Monadnock 

235 

53 

53  -272 

0  "09 

-f  0  -032 

53  -30 

—0  -03 

53  '27 

Pi 

obable  error  of  a 

single 

observation  y  D.  and  A'. )  of  a 

direction,  < 

,  =  -0" 

-75.     Circle 

used  in 

■V  posit 

ions,  in  1848  and 

in 

i860 

*  The  station  was  occupied  l)y  Prof.  E.  T.  Quimby  in  1S7S,  l>ut  only  in  connection  with  the  .sur\-ey  of  New  Hampshire:  it 
was  reoccupied  in  September.  1S97,  bj-  As.sistant  .\.  T.  Mosraan,  in  connection  with  western  work  in  Vermont. 

fThe  station  was  occupied  by  I'rof.  E.  T.  Ouimby  in  July,  187-'.  in  connection  with  the  s>ir\ey  of  New  Hampshire. 
He  used  25'-i"  theodolite  No.  31.     He  sighted  Monadnock.  and  Patuccawa,  but  for  these  obsereations  w-e  have  no  use  here 


iiS 


THE    EASTERN    OBLIQUE    ARC. 


Ahslracts  of  horizon /a!  directions  as  obscri'ed  and  adjusted  at  the  principal  stations  between  the  Epping 
base  net,  the  3lassachiisetts  base,  and  the  Fire  Island  base  net,  /S-/^-/SS2 — continned. 

Thompson,  Essex  County,  Massachusetts.     October  15  to  November   24,  1S46,  and  July  27  to  August 
23,  1847.     75"^"'  direction  theodolite  No.  i.     A.  D.  Bache,  observer. 


iber  of 
ctions. 

objects  observ 

ed. 

Resulting  direc-       ,^             ;. 

Reductions 
to  sea  level. 

Resulting 
seconds. 

Corrections 

from 
figure  ad- 
justment. 

Final 
seconds. 

0 

/ 

// 

// 

// 

// 

// 

// 

73 

Manoniet 

0 

00 

00  ■QOO 

rfcO-l8 

—0  '002 

GO  '00 

-fo'IO 

GO  •JO 

74 

Blue  Hill 

44 

15 

19752 

O'll 

4-0  ■Oil 

1976 

+  0-I4 

19-90 

75 

Wachusett 
Holt 

90 
104 

52 

48 

38  782 

53  '491 

0-I2 
0-13 

+  0-0I0 

38  -79 

0  '00 

38 -79 

76 

Unkonoonuc 
Patuccawa 

129 

154 

22 
45 

49  757 
22  -283 

0  •14 
0  '12 

—  0  -021 

49-74 

+0  -11 

49-85 

77 

Gunstock 

161 

29 

50  -943 

0-I5 

-0  -035 

50-91 

-0-23 

50-68 

Aziijuith  Mark, 

west 

1.S6 

35 

38  -458 

0  '19 



.... 

Aziinuth  Mark 

east 

190 

40 

47  -449 

0-29 

78 

Aganienticus 
Isle  of  Shoals 

191 
201 

13 
26 

43  -021 
34-383 

0  '12 
0  'II 

+  0  '001 

43-02 

— o'i4 

42-88 

Circle  used  in  III  positions  in  1S46. 

JVachnsett,  Worcester  County,  Massachusetts.     September  13  to  October  16,   i860.     75'='"   direction 
theodolite  No.  i.     A.  D.  Bache  and  G.  W.  Dean,  observers. 


Azimuth  Mark 

0 

00 

GO  'OOG 

=bo-io 

65 

Bald  Hill 

iS 

32 

53-177 

0  -20 

66 

Mount  Tom 

60 

52 

05  -024 

0-34 

67 

Monadnock 

150 

38 

43  -050 

0-13 

68 

Gunstock 

194 

20 

24  -085 

G  '14 

69 

Unkonoonuc 

198 

09 

22  750 

0-13 

Patuccawa 

212 

49 

54  -036 

0  '12 

Holt 

249 

13 

40  -236 

0-15 

70 

Thompson 

255 

42 

43  -548 

0-I7 

71 

Blue  Hill 

2S9 

46 

57  -469 

0-13 

72 

Beaconpole 

320 

47 

46  -S73 

0-I2 

+0  '017 
+0  -016 

—  G  '042 
+0  '027 
+  G  -018 


OG  'OO 
53-19 
05-04 

43  -oi 
24  'ii 
22  77 


4-0  '00 1 

— o  '009 
— o  '009 


43  -55 
57-46 
46  -86 


+0-G7 
-I  -17 
-fo-23 
40-13 
— o  -07 


-0-05 

'O  -G2 
-0-15 


Circle  used  in  V  positions. 


53-26 
03-87 
43-24 
24-24 
22  -70 


43-50 
57-44 
47-01 


Blue  Hill,  Norfolk    County,  Massachusetts.      September    14   to    October    19,   1845.      75'^"'   direction 

theodolite  No.  i.     A.  D.  Bache,  observer. 


79 

Manoniet 

So 

Copecut 

81 

Great  Meadow 

82 

Beaconpole 

83 

■Wachusett 

84 

Unkonoonuc 

Holt 

Azimuth  Mark 

85 

Thompson 

0 

00 

// 

GO  -GOG 

// 
±0-11 

// 
—0-007 

// 

// 

+G-I4 

// 

0 

59-99 

00-13 

49 

17 

23-167 

0-14 

—0  -ooi 

23-17 

-40-03 

23-20 

67 

01 

11-778 

G-II 

-fO  -G02 

II  -78 

—0  -OI 

II  -77 

103 

II 

18-606 

0  -14 

40-010 

18-62 

-0-52 

18-10 

170 

05 

20  -382 

G  -12 

—  0  -028 

20-35 

-t-0-20 

20-55 

209 

46 

13  -547 

0-13 

—0-018 

13-53 

-fo-23 

13-76 

234 

48 

06-131 

G  -10 

.... 

236 

05 

03  -497 

G  -09 

269 

23 

57  -425 

o-io 

4-0-005 

57-43 

—0-07 

57-36 

Circle  used  in  ^VI  positions. 


THK    MAIN    TRIANGULATION. 


119 


Abs/rads  0/  liorirjoiita/  directions  as  observed  and  adjusted  at  the  principal  stations  between  the  Epping 
base  net,  the  Afassachnsctts  base,  and  the  Fire  Island  base  net,  1844-/882 — continued. 

Great  Meadow,  Bristol  County,  Massachusetts.     May  7  to  27,  1S45.     75*^'"  direction  theodolite  No.  i. 

A.  D.  Bache,  observer. 

Resultiiif!  direc-         Ar,r.rr,vi  Corroctioii.s 

Number  of  ,.k;..„*..  „k„<.„.<.^  tious  from  „r,te  nrolV    Keductions     Resulting  f 


directions. 


Objects  observed. 


stati^i  adjust-       ^„^,^  ^.^^^^ 


.,^....^i.«...,     .^^.,. J,  .roni  Final 

to  sea  level,      seconds.        figure  ad-        seconds, 
justment. 


104 
101 
102 

103 


Copecut 
Beaconpole 
Massachusetts  North 

Base 
Blue  Hill 


o  00  00  'oaj 

160  29  59 'SSI 

219  19  14-351 

229  39  39  'oSo 


±0  '14 
0-15 

o  19 

o  '14 


—  O  TX36 

— o  '009 

o  "000 
+0  -005 


59 '99 
59 '34 

14-35 
39.  oS 


-o  -28 

+0  -28 

— o  -24 
-t-o  -20 


59'7i 
59-62 

14-11 
39  ■2.S 


Circle  used  in  III  positions. 


Copecut,  Bri.stol  County,  Massachu.setts.     September  7  to  October  8,  1844.     75'" 

No.  I.     A.  D.  Bache,  oh.server. 


direction  theodolite 


92 

Blue  Hill   and 

Azi- 

0 

/ 

// 

// 

// 

// 

// 

// 

inuth  Mark 

0 

GO 

00  '000 

±0-13 

—0  '002 

00  -oo 

—0-19 

59 -Si 

93 

Manoniet 

64 

oS 

37-851 

0  -16 

+0  '006 

37  -86 

-rO-QI 

37-87 

Indian 

140 

03 

44  -563 

0-15 

90 

Beaconpole 

318 

01 

oS  -556 

0-13 

—  Q-OIO 

oS-55 

-0-17 

08-38 

91 

Great  Meadow 

328 

04 

06  -825 

0-15 

—0-005 

06  -82 

+0-39 

07  -21 

Circle  used  in  III  positions. 

Manoniet,  Plymouth    County,  Massachusetts.     August    25   to   September    11,  1845.      75'^'"    direction 

theodolite  No.  i.     A.  U.  Bache,  observer. 


Provincetown 

0 

00 

00  -ooo 

d=o  -11 

Indian 

120 

13 

21  -474 

0  'ID 

86 

Copecut 

172 

29 

05  -212 

0-T7 

87 

Beaconj.ole 

209 

03 

27  '009 

0  -16 

88 

Blue  Hill 

239 

03 

09  -898 

0  -10 

89 

Thompson 

284 

II 

54  '745 

0-13 

Circle  used  in  VI  positions. 


-fo  -006 
— o.  002 
— o  -on 
— o  -001 


05  -22 

27  01 

09  89 

54-74 


Massachusetts  South  Base,  Bristol  County,  Massachusetts.     September  9  to 

theodolite  No.  11.     E.  Blunt,  observer. 


+0-07 

+0-I0 

— o  -08 
— o  -06 


05-29 
27-11 
09  Si 
54-68 


1845- 


25 '"'  repeat ins^ 


105 

Beaconpole 

0    00 

00  -cx^ 

106 

Massachusetts  North 

Base 

81     00 

16-66 

0-45       (-0-004 


59  "99 


16-66 


3/assachusetts  North  Base,  Bristol  County,  Massachusetts.     September  19  to  29,  1S45 

theodolite  No.  11.     E.  Blunt,  observer. 


— o  -20 

-f  o  -20 

!5 


59  79 

16  -89 
repeating 


107 

Great  Meadow 

0 

00    cx)-ooo 

=to  -35 

0  -ooo 

00  -oo 

-fo-26 

00 -26 

108 

INIassachusetts  South 

Base 

25 

16    31  -173 

0  -35 

+0  -002 

31  -iS 

— 009 

31  -09 

109 

Beaconpole 

70 

09    29  -s  1 2 

0  -35 

ro  -006 

29  82 

-0-I7 

29  -65 

I20 


THE    EASTERN    OBLIQUE    ARC. 


.-Ibstracts  of  horizontal  diirctions  as  observed  and  adjusted  at  the  principal  stations  hetiveen  the  Eppitis; 
base  net,  the  Massachusetts  base,  and  the  Fire  /stand  base  net,  /iV^^-z^^i"— continued. 

Beaconpole,  Providence  County,  Rhode  Island.      October  19  to  November  23,  1844.     75 ""  direction 

theodolite  No.  i.     A.  D.  Bache,  observer. 


Number  of 
directions. 

Objects  observed. 

Resulting  direc- 
tions from 
station  adjust- 
ment. 

Appro.Ki 
mate  prob- 
able errors. 

Reductions 
to  sea  level. 

Resulting 
seconds. 

Corrections 
from 
figure  ad- 
justment. 

Final 
seconds. 

Wachusett 

0 
0 

f 

00 

// 
GQ-OOO 

// 
d=0  '11 

// 
-0  -034 

f  f 

// 
—0  -26 

" 

94 

59 '97 

5971 

Azimuth  Mark 

35 

12 

22  -656 

o-i6 

95 

Blue  Hill 

82 

05 

13  "35' 

O'll 

+  0-0I2 

13  -36 

+0-40 

1376 

96 

Massachusetts  North 

Base 

105 

44 

12  '597 

0-15 

-f  0  -002 

12  '60 

+0-17 

12-77 

97 

Maiiomet 

1 28 

54 

18-252 

0  -16 

— 0  "001 

18-25 

-0-28 

17-97 

98 

Great  Meadow 

156 

45 

30  -025 

0-09 

—0  -005 

30-02 

-0-I5 

29.  87 

99 

Massachusetts  South 

Base 

159 

50 

57  •«43 

0  TI 

—  0  '002 

57-84 

—0-03 

57 -'^i 

100 

Copecut 

166 

12 

31  431 

o-io 

— o"oo6 

31  -42 

+0-13 

31  -55 

Circle  used  in  IH  positions. 
JMonadnoc/c;*  Cheshire  County,  New  Hamp.shire.     July  21  to  August  15,  r86i.     75* 


direction  theod- 


60 

Gunstock 

61 

Unkonoonuc 

62 

Wachusett 

63 

Bald  Hill 

64 

Mount  Tom 

olite  No. 

.     G.  W. 

Dean, 

observer. 

0 

/ 
00 

// 

GO  -QGO 

±0  -lo 

// 
-f  0  -042 

// 
00-04 

~o-i4 

/' 

0 

59 '90 

32 

54 

52  '457 

0  -19 

-f  0  -G14 

52-47 

O-GO 

52-47 

117 

01 

19-427 

0  -10 

—0  -026 

19  -40 

—  G-I2 

19  -.-28 

145 

06 

44-724 

0  -09 

+0  -004 

44  73 

+  0  -35 

45  -08 

173 

46 

06  -97 1 

0  -ir 

4-0  -019 

06  -99 

—  0  -08 

g6  -91 

nervation  (  D.  and  A' 

)  of  a 

direction,  er- 

=  ±0^.67. 

Circle 

used  in  V 

positions. 

Mount  Tom,]-  Tolland   County,  Connecticut.     July  11   to  August  16,  1862.     75""  direction  theodolite 
No.  I.     G.  W.  Dean  and  R.  ¥^.  Halter,  observers. 


OG  OG  -000 

45  13  -052 

28  4G  -690 

52  53  -979 

18  15  -047 

163     34  58  -584 
Circle  used  in  V  positions. 

Batd  Hill,  ToUaiid  County,  Connecticut.  September    12  to   25,  1861,  and   May   22  to  June   7,   1S64. 
y-cm  direction  theodolite  No.  i.     G.  W.  Dean,  olxserver. 


115 

Monadnock 

0 

Azituuth  Mark 

4 

TI6 

■Wachu-sett 

33 

117 

Bald  Hill 

95 

118 

Box  Hill 

129 

119 

Sandford 

163 

zhO  -10 

J-G  -052 

GO -05 

-f  0-12 

00-17 

0-08 

0  -09 

+  0  -G27 

40.  72 

+0  -30 

41  -02 

o'oS 

-0  -023 

53  -96 

0  -00 

53-96 

0  -09 

—  0  -009 

15  -04 

-0-13 

14-91 

0  -12 

+  0  -009 

58-59 

-0-33 

58-26 

no 

Box  Hill 

G     00     OG  -GOG 

±o-g8 

-f  0-015 

00  -02 

+  0-21 

00-23 

III 

Ivy 

34     47     46  -780 

0  -12 

+0-0G7 

46-79 

-fo-28 

47-07 

112 

Mount  Tom 

So     50     44  -995 

G  'IG 

~o  -022 

44-97 

—0-05 

44-92 

'13 

Monadnock 

136     18     39  -740 

0-I4 

+  G  -G09 

39-75 

— o-6i 

39-14 

114 

Wachirsett 

156     07     28  -560 

0  -12 

+  0  -G2S 

28-59 

-+-0  '11 

28-70 

Circle  used  in  "V  positions  in 

1 86 1  and  1864. 

♦This  station  was  occupied  by  Prof.  E.  T.  Quimby  in  June,  1872,  in  connection  with  the  survey  of  New  Hampshire. 
In  September,  1878,  the  party  of  Assistant  R.  D.  Cutts  reoccupied  the  station,  but  neither  of  these  observers  made  any 
additions  to  the  measures  of  the  oblique  arc. 

t  This  station  wasoccupied  in  June  and  July,  1877,  by  .\ssistant  R.  D.  Cutts  in  connection  with  the  survey  of  Vermont. 


THE    MAIN    TRIANGULATION. 


121 


Abstracts  of  horizontal  directions  as  nt)scrvc(l  aiict  adjusted  at  the  principal  stations  between  the  Eppiu)( 
base  net,  the  Alassachusetts  base,  and  the  Fire  Island  base  net,  /H^-f-/8H2 — continuerl. 


Box  Hill,  Tolland  County,  Connecticut.      Octolier  9  to  2.S,   1861. 

G.  W.  Dean,  observer. 


75""  direction  theodolite  No.  i. 


Number  of 
directions. 


Objects  ob.served. 

Sandford 
Ivy 

Mount  Tom 
Bald  Hill 
Circle  used  in  V  positions. 


120 
121 
122 
123 


Resulting  direc- 
tions from 
statiiiii   adjust- 
ment. 


O  00  00  "000 

49  35  39'««i 

114  15  55751 

179  59  54 '087 


Ajjproxi- 
mate  prolj- 
al>lccrrors. 

Reductions 
to  sea  level. 

Resulting 
.seconds. 

Corrections 
from 
figure  ad- 
justment. 

Final 
seconds. 

// 

// 

// 

// 

// 

±0-13 

-t-o-oi7 

CX3  '02 

-fO  TO 

00'12 

0  -1  I 

—0  -007 

39 '^7 

-o-o8 

39  78 

0  'II 

-0-013 

55  74 

-^028 

56  02 

0    10 

+0  -024 

54   1 1 

— 0-2S 

53  •-'^3 

Ivy,  Litchfield  County,  Connecticut.     June  29  to  August   12,  1863.     75  "' direction  theodolite  No.  i. 

G.  W.  Dean,  observer. 


124 

Bald  Hill 

125 

Box  Hill 

126 

Sandford 

127 

Wooster 

O  00  00  '000  rbO  'oS  +0  '007 

14  48  02 '805  0'09  — o '004 

71  09  55 '842  0-09  —0-013 

118  50  47-463  0-I2  -I-0-0I2 


Circle  used  in  V  positions. 


00 -or 

—0-04 

59  97 

02  -So 

-0-13 

02  -67 

55-83 

—  0  -12 

55  71 

47  -48 

-o'33 

47  -81 

Sandford,  New  Haven  County,  Connecticut.     vSepteinber  9  to  November  4,  1S62.     75^'"  direction  theo- 
dolite No.  I.     G.  W.  Dean,  observer. 


Number 
of  direc- 
tions. 

Objects  observed. 

Resulting 
directions  from 
station  adjust- 
ment. 

Approx- 
imate 

probable 
error. 

Reduc- 
tion to 
sea  level 

Correct- 
ed direc- 
tions. 

Correc- 
tions 
from  net 
adjust- 
ment. 

Result- 
ing direc- 
tions. 

Correc- 
tions 
from  fig- 
ure ad- 
justment. 

Final 
seconds. 

Ruland 

0 

00 

OO'OOO 

±o-ti 

—0-264 

59-74 

West  Hills* 

23 

24 

4!  '547 
-f  0  -ooS 

0-12 

-1-0 -482 

42-04 

Tashua 

42 

36 

58-413 

0-12 

-Ho -01 1 

5S  -424 

-0  -330 

5^-09 

Wooster 

69 

03 

33'ii3 

0-24 

-(-0  -009 

33-122 

+0  -356 

33-4S 

Azimuth  Mark 

85 

20 

30. 246 

0-15 

128 

Ivy 

147 

34 

47  -646 

0-15 

—0  '024 

47-62 

-1-0 -25 

47-57 

129 

Mount  Tom 

190 

09 

54 '5^1 

0-12 

-1-0 -012 

54  59 

-l-o-ii 

5470 

130 

Box  Hill 

22: 

37 

22-062 

O'lO 

-1-0 -016 

22 -oS 

-1-0  02 

22-10 

Circle  used  in  V  positions. 

Wooster,  Fairfield  County,  Connecticut.    July  14  to  October  10,  1S64.     75" 

G.  W.  Dean,  observer. 


direction  theodolite  No.  i. 


131 

Ivy 

0 

00 

00  -000 

±0-07 

Sandford 

53 

47 

59-20S 

0  -07 

Tashua 

95 

57 

47  652 

o-oS 

Ruland 

124 

51 

45  -93S 

o'oS 

West  Hills* 

154 

10 

3S  -493 
+0-032 

0-07 

Circle  used  in 

V 

positions. 

-f  0  -020            00  -02 

-1-0 -009        59 '217  -o_o69  59-15 

-0-009        47643  +0-285  47-93 

+0  005  45-94 

-0-147  38-3^ 


*The  correction  to  direction  of  West  Hills  Is  for  eccentricity. 


—0-29 


59 


122 


THE    EASTERN    OBLIQUE    ARC. 


Observation  equations. 


I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 

XIV 

XV 

XVI 

XVII 

XVIII 

XIX 

XX 

XXI 

XXII 

XXIII 

XXIV 

XXV 

XXVI 

XXVII 

XXVIII 

XXIX 

XXX 

XXXI 

XXXII 

XXXIII 

XXXIV 

XXXV 

XXXVI 

XXXVII 

XXXVIII 

XXXIX 

XL 

XLI 

XLII 


0  = 

o= 
o= 

0  = 

o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 
o= 


— o  -45- 
+o  -46- 
-o  -38- 
+0  -09- 
-o  -08  - 
-o  -66- 
+0  -49- 
+0-07- 


(i)  + 
(2)  + 
(i)  + 
(7)  + 

(7)  + 

(8)  + 


(4)- 
(2)- 
(9)- 
(8)- 
(9)^ 


;i4)+ 
(5)+ 

(6)  + 

:i2)+ 


,15) 

(6) 

(7)- 

:r3)- 


(io)+  (12)- 
(i8)+  {20)- 
+0-85-  (21)+  (22)- 
+0-09-  (19)+  {20)- 
-]  -42-   (31)+   (32)- 

+  I-20-  {36)+  (37)- 

-2  ■02-  (29)+  (30)- 

+  1  -22-  (30)-f-  (31)- 

+  0-39-  (44)+  (45)- 


(ii)+  (13)- 

{i6)+  (18)- 

(17)+  (20)- 

(22)+  (23)- 

(27)+  (29)- 

(26)+  (29)- 

(34)+  (35)-   (41 

(43)+  (44)-   (51 


(49) 
(45) 
(55) 
(45) 


+  1  -05- 
+0-03- 
— o  '27 
+0-6I- 
—0-23-  (46)- 
+0-6I-  (57)- 
+0-69  - 
+0  -37- 

-I  '55- 
—0-25  — 
— o  '62— 

+0  -84- 
+0-07- 
+  1  -lo— 


(36)+ 
(42)+ 

(49)  + 
(54)  + 
(55)- 
(69)  + 


(50)- 

(46)  + 

(57)- 

(47)- 

(48)- 

(58)- 

(55)+  (56)- 

(70)^   (71)- 

(71)+   (72)- 

(73)+  (74)  + 

(86)+   (87)- 

(80)+   (82)- 

(79)+  (80)-  (86)+  (88)-^ 
(80)+  (81)-  (91)+  (92)-- 
-I -41-  (90)+  (9i)~  (98)  +  (ioo)  + 
+  1-28-  (96)+  (98)-(ioi)  +  (io2)- 
-oTi-  (96)+  (99)-(io5)  +  (io6)- 
-1-62-  (62)+  (64)-  (66)+  (67)- 
+  I-IO-   (63)+  (64)-(ii2)  +  (ii3)- 


+  1-37-  (65)  + 
+o'96— ( iio)  + 

+0  '22-  (lI0)  + 

+0-II— (ii8)  + 
+0-41  — (120)  + 
—0-99— (126)  + 


(66)- 
(112)- 
(III)- 

(119)- 
(121)- 
(127)- 


-(II2)  +  (II4)- 

-(ii7)  +  (ii8)- 

-(I2l)+^I23)- 

-  (120)+  (122)  — 

-(I25)  +  (I26)- 

-(i28)-(i3i) 


(13 
(16 

(24 

(23 

(26 

(26 

(38 
(38 


(38)-  (52 

(44)--   (51 
(51)-   (77 


(76 
(76 
(75 
(75 
(60 

(67 
(84 
(83 
(94 
(88 

(97 


(55)-- 

(59)- 

(70)- 

(68)+   (70)- 

(58)+  (59)- 
(6i)+  (62)- 
(74)+  (76)- 
(74)+  (75)- 
(82)+   (83)- 

(79)-  (85)- 
(90)+  (93)-- 
(90)+  (92)-  (95 

(92 
(103 

( lOI 

( 107 
(108 

(115 
("5 
(116 
( 122 
(124 
( 129 
(128 


+  (15) 
+  (17) 
+  (25) 
+  (24) 
+  (28) 
+  (27) 
+  (40) 
+  (39) 
+  (42) 
+  (53) 
+  (53) 
+  (52) 
+  (78) 
+  (78) 
+  (77) 
+  (76) 
+  (77) 
+  (61) 
H-  (69) 
+  (85) 
+  (85) 
+  (95) 
+  (89) 
100) 
100) 

(93) 
104) 
104) 
109) 
109) 
116) 
117) 
117) 
123) 
125) 
130) 
130) 


+ 


-3'8-2-77(i)+3"39(2)+4-29(3)-3'35(4)  -i  •43(  i3)  +  i  •89(14) -o -46(15) 
-I  7+o-2i(ii)  +  i  -28(12)  — I  •49(i3)-3-3o(i6)+4-i4(i7)—o-84(i8)-o -79(23) 
+4 -14(24) -3 '35(25) 


THE    MAIN    TRIANGULATION. 

Observation  ftjucUioiis — coniiiiue'l. 


123 


I 


XLIII 

o=  — 1 

+0 

XLIV 

o=— 0 

+4 

XLV 

0=  J  I 

XLVI 

—  1 
o=~6 

+  3 

XLVII 

o=-|-o 

+  3 

XLVIII 

o=  — I 

— 0 

XLIX 

o=  — I 

+3 

Iv 

0=  +  2 

+  1 

LI 

o=— 0 

+5 

WI 

o=  — 2 

+  2 

LIII 

o=— 0 

— 0 

IvIV 

o=  +  i 

+  4 

LV 

o=  — I 

+7 

LVI 

o=+5 

+  2 

+2 

—  I 

— 0 

+0 

+  1 

—  I 

—0 

+0 

LVII 

0=+2 

—  2 

—  2 

+  0 

+0 

-3 

+  1 

•S2J-4  •5S6(  10)  -4-864(11)  fo -278(12)^0  •2401 17)— <j-455(  18) -o -215(20) 
1-168(26)     3  ■9i8(27)+3 -750(28) 

•8-4-70(18)  I  6 -85 (19) ---2 -15(20) -I  -68(26)--3-53(27)-  1  -85 (29) -o -46(38) 

■46(39)-4 '00(40) 

-7-4-o8(i9)-|  4-08(20)1  3-59(26)     3  •59(32)-4-4o(33)  +  5  ■68(34)-! -28(35) 

•54(37)1-3  •15(38)-!  ■6i(39)-3 -10(41) +6 -i8(42)-3 -08(43) 

-2-2-03(29)  +  !  -96(3o)+o-o7(3i)-3-o8(42)+4 -94(43)-!  •86(44)-o -16(51) 

-2o(52)-3 -04(53) 
i-8-2-87(44)+3-39(45)-o-52(46)+3-32(54)-i  -73(55)--i  -59(59)-!  -13(76) 

-69(77)-2 -56(78) 

-23-o-2i6(45)+3  -472(46)-3  -256(47)    -3  -i56(68)-3  -29fj(69)-o -134(70) 
'  -265(75)+o  -6oo(76)-o  -335(77) 

-7-2-i6(45)  +  7-i2(46)-4-96(48)  +  3-25(6o)+3-47(6i)-o-22|62)--i  -93167) 

-27(69)-!  •34(7o)-2-65(75)+6-oo(76)-3 -35(77) 

-4-2-98(55)+4-83(56)-i-85(57)+o-o6(69)+3-ii(7o)-3-i7(7i)-i  -81(74) 

-99(75)-o-!8(76) 
I -7-3- II  (7o)+6 -61(71  )-3-5o(72)-2 -16(73) -r4 -15(74)-!  ■99(  75) -3 -65(87) 

-74(88)-2-o9(89)-o-29(94)+2-27(95)~i  -98(97) 

-0+0  •49(79)  +  !  -54(8o)-2  -o3(82)-2  -84(86)+6  •49(87)-~3  -65(88)  -2  -95(90) 

-34(92)40-61(93) 

-61—0  -659(8o)+o -947(81  )—o  -288(82)  —  I  -188(90)  -t-i  -526(91 )— o  -338(92) 
'■o58(95)  +  i  -323(98)  — I  -265(100) 

•4-2  •56(62)+3  •94(63)-!  •38(64)-o  •55(ii2)  +  5  -84(  ii3)-5  ■29(  1 14) -3  -iS(  iis)' 
,  -28(116)-!  -10(117) 

-0-2 -69( iio)+3  •03( 111 )-o^34(ii2)-3  •19(117)^6-28(118) -3 -09(1 19) 

•97(1 24) -9  •37(125)  +  !  •4o(  i26)+o  •60(128) -3  •44(  129)  T-2 -84(130) 

■7       2  -77(  I)  +2  ■77(2)+o  -94(4)  +2  ■46(5)-2  -46(6)-2  -31  (8) 

•3i(9)+o^2i(i!)+o-25(i3)— 0-46(15) +0-84(16)— 2  •99(18) 

-15(20)- I  •56(21)  +  !  •56(22)  +  3^35(24)-3^35(25)  +  !  -68(26) 

-68(27)+o  -o7(29)-o  -07(3!  )-2  -o4(36)  +  2  -04(37)^0  -46(38) 
I  -46(4o)+3  •o8(42)-3  -08(43)  -o  •52(44)+o  •52(46)-o  ^86(49) 

•86(5o)+o-i6(5i)-o -16(53)-!  •59(54)-! -85(56)  +  ! -85(57) 

-59(59)-o-o6(69)-3^44(7i)+3-5o(72)~o^iS(74)-i-i  •31(76) 

•!3(78)-2^88(8i)  +  2 -88(82)  +  !  -24(84)-!  -24(85)^0-29(94) 
'-29(95)-!  ■52(96)  +  !  •52(99)~o^48(ioi)  +  i  •28(!O2)-o^So(i03) 

-33(!05)-o  •33(  io6)  +  o  •76(  107)  -o  •76(  109) 

-6+1  -85(56)■-3-72(57)^  I  •87(58)+o  •22(61)-!  -60(62)  j-i  -38(64) 

-31(65)  +2  •3i(66)+3  ^50(71 )  -3  •5o(72)  +  2  •88(81) -2  ^88(82) 

-54(S3)  +  2^54(S4)-o^29(94)+o^29(95)  +  i  •52(96)-!  ^52(99) 
1  •48(  loi  )-i  •28(  102)  +0  -8o(  103) -o  -33(  !05)+o  •33( io6)-o  •76(  107) 
1  •76(  109) -o  •34(  1 10) 4  o  •89(  112)0  -55(  1 14)+3  •i8(  115)    -3  •iS(  1 16) 

-09(118)^3  •09(119)-!  •79(120)  +  !  -79(i2i)+o-95(i22)-o -95(123) 

•40(125)  -3  -32(126)  +  !  ■92(i27)+3  •44(i29)-3  -44(130)^1  -54(131) 


124 


THE    EASTERN    OBLIQUE    ARC. 


Correlate  equations. 


(I 

(2 

(3 

(4 

(5 

(6 

(7 

(8 

(9 

( lo 

( n 

( 12 

(13 

(14 

(15 

{16 

(17 
(18 

(19 
(20 
(21 
(22 
(23 
(24 
(25 
(26 
(27 
(28 
{29 
(30 
(31 
(32 
(33 
(34 
(35 
(36 
(37 
(38 
(39 
(40, 


o  1^ 
o 

=0  -St  -C,-C3-2  •77C4,-2  -77056) 

=0  -gl  -C3+C3i  3  •39C4,  +  2  •77C56) 

=o-9(+C,^4-29C4,) 

=  1  •i(+C.-3-35C4,+o-94CV) 

=0 -St -C.+2 -46056) 

=o-8(+C,-C3-2-46C56) 

=o-8(+C3-C4-C5) 

=0-9{+C5-C6-2-3lC56) 
=  0-9(-|-C4  +  C6+2-3lC56) 

=  i-2(-C,+4-586C43) 

=  1  ■i(— C5+0-2lC4i,— 4  -864C43+0-21C56) 

=0  ■9(  -C4+C,+  i  -28C4.+0  -27SC43) 

=o-8(-C3+C4+C5-i  •43C4,-i  •49C42+0-25C56) 

=  i-i(-C.  +  i-89C4,) 

=0  •8(  +C,+C3-o  -46C41-0  -46056) 

=  1  -i(-C4-C6-3-3oC4,+o-84C56) 

=  1  •o(+C4~-C7+4-i4C4,+o-24oC43) 

=  1  -o(+C6~Ce-o-S4C4,-o-455C4,-4-7oC44-2-99C;6) 

=  2  -o(  -Cio+6  -85C44-4  -08C45) 

=  1  •o(+C7+C8  +  C,o+o-2i5C43-2-i5C44+4 -08045+2  -15056) 

=o-9(-Cg-i-56C56) 

=o-9(-C8+C,4-i-56C56) 

=o-8(-C6+C8-^o-79C4.) 

=  i-i(-C5+C6+4-i4C4.+3-35C56) 

=  i-i(  +  C5-3-35C4.-3-35C56) 

=o-8(-C7-Cs-C,o+o-i68C43-i  •68C44+3  -59C45+r  -68C56) 

=0  •9(  +  C8-C9-3  -918C43+3  -53C44-1  -SSCjo) 

=o-9(+C7+3-75oC43) 

=o-S(^C,+C,o-C,3-i  -85C44-2  -03C46+0-07C56) 

=o-9(+C,3-C,4+i-96C46) 

=0  -8(  — C„+C,4-f  o  -07C46— o  -07C56) 

=  i-5(+C.,-3-59C45) 

=o-8(-4-4oC45) 

=o-9(-C„+5-68C4s) 

=o-9(+C„-i-28C45) 

=  i-i(— C„— C,3— 2-04C56) 

=  i-3(  +C,=—  I -54C45  +  2-04C56) 

=o-9(-Cc,-C,o+C,3-o-46C44+3-i5C45+o-46C5s) 

=o-9(+C,o  +4-46C44"i-6iC45) 

=  I  -o{  +C3— 4-00C44  -0-46056) 


THE    MAIN    TRIANGULATION. 


125 


o 


u 


OS.- 


Correlate  equations — coiiliiiued. 


-C,:-3-I0C,5) 

+C„-C,4+6-i8Q5-3-o8CV+3-oSCs6) 
— C,2— 3-oSC4^+4-94C46— 3'0'SC56 ) 
+C„+C,4-C,5-r86C4,-2\S7C„-o-52C56) 

+  C,5^C,7— 0,9  +  3-39047— 0-2l6C48-2-l6C45) 

+  C,7-C20-O-52C47  +  3-472C48  +  7'I2C45  +  O-52C56) 

+C,9-3-256C48) 
+  C.,,-4-96C49) 
-C.s-C,6-o-86C56) 

+  C,6  +  0-S6C56) 

-C..-C.4  +  C,5-0-l6C46+0-l6C56) 

-C,3+C.4  +  3-20C46) 

+Ci:,+C,3-3-o4C46— 0-I6C56) 
C,6+3'32C47-r59C56) 

+  C:6+C,7-C,8-C..-  I  73047-2-98050) 

+C..+4-83C50- 1  •85056+1-85057) 
+  0,8-C\,-i-8505o+i-85056-3"72057) 
0,0+0.,  + 1 -87057) 

0,7  +  0.0-  I  •59C47+  I  '59^56) 
O3o-3'25C49) 

0.o-0„  +  3-47C49+o-22057) 
+  0^,-033-0-22049- 2-56054-1-60057) 
C34-3 -94054) 

+  033+034-I-3SC54-tI-3S057) 

C35-2-3IC57) 
033  +  0,5+2-31057) 
-0„  +  033-I-93C49) 

0,9-3-156048) 

0,8+0.,+3-29o048+3-27049^o-o605„-o-o6056) 
+0,8+0,9-0,3-0-134048- 1  -34049+3-1 105„-3- 1 1O5, ) 
+0,3-0.4-3-i705„+6-6i05,-3-44C56+3-5oC57) 
+C=4-3'5o05,  +  3-5o056-3-5o057) 

=  1  ■!(— 0,5  — 2-I6O5,) 

-C3.-C%3+0.5-i  •81050+4- iSCs.-o-iSOjs) 
-0,8-0,9+0.3-o-265048-2-65049+ 1  -99050-1  •99O5. ) 

—  0,6  — 0,7  +  0,8  +  0..- I  •I3O47+O-600O48+6-OOO49— 0-18050—1-31056) 

-0,5+0,7+C.9+3^69C47-o-335048-3-35049) 

+0,5+0,6-2-56047- 1  -13056) 

+0.3-C.8+o-49C5») 
-O.7+C.8-C.9+ 1  •54C5.-o^659053) 


(41 

)=o-8( 

(42 

=o-8( 

(43 

=o-8( 

(44 

=o-9( 

(45 

=o-9( 

(46) 

=o-7( 

(47 

=o-8( 

(48 

=o-7( 

(49 

=o-9(- 

(50 

=  i-i(- 

(51 

=o-9( 

(52 

=o-9(- 

(53 

=o-9(- 

(54 

=o-9( 

(55) 

=o-8(- 

(56^ 

=  i-o(- 

(57) 

=o-7(- 

(58 

=o-8{- 

(59^ 

=0-7  (- 

(60 

=o-S( 

(61 

=o-S(- 

(62 

=o-8(- 

(63^ 

=o-8( 

(64 

=o-8(- 

(65 

=  i-3(- 

(66 

=  2-5( 

(67 

=o-9{ 

(68^ 

=o-9(- 

(69) 

=o-9( 

(70 

=  i-i(- 

(71 

=o-9{ 

(72 

=o-9( 

(73 

=  1  ■!( 

(74 

=o-8( 

(75 

)=o-9( 

(76 

)=o-9( 

(77^ 

=  i-o( 

(78 

)=o-9( 

(79 

)=o-S( 

(80 

)=o-9( 

126 


THE    EASTERN    OBLIQUE    ARC, 


Correlate  equations — continued , 


u 
(Si) 

(82) 

(83) 
(84) 
(85) 
(86) 

(87) 
(88) 

(89) 
(90) 
(91) 
(92) 
(93) 
(94) 
(95) 
(96) 
(97) 
(98) 
(99) 
(100) 

(lOl) 

(102) 
( 103 ) 
(104) 
(105) 
(106) 
(107) 
(108) 

( 109) 
(no) 
(in) 
(112) 
(113) 
(114) 
(115) 
(116) 

(117) 
(118) 

(119) 
(120) 


"o  C 
a;  > 

0 

=o-8 
=0-9 
=0-9 
=0-9 
=o-8 
=  i'i 
=  l'o 
=o-8 
=0-9 
=0-9 
=  i"o 
=0-91 

=  I"Oi 

=o-8 
=o-8 
=  i-o 

=  I'0' 

=o-8 
=o-8 
=o-8 
=  i-oi 

=  I'2 
=0-9 
=0-91 

=3-8i 
=3-8 
=2-51 

=  2-5' 

=  2-5 
=o7' 
=0-9 
=o-8' 
=0-9 
=0-9 
=o-8 
=o-8 
=07 
=o-S 
=0-9 
=0-9 


+C=g-t-o-947C53-2-SSC56+2-88C5 


—C,4-!-C2-— 2-0305 


-2-S8C55J-2-SSC56-2-88C5 


-C.,+a4-2-54C5,) 

-C22^I-24C56+2-54C57) 
^C,,+  C,5-C=5-I-24C56) 

-C.6-C.8~2-84C5.) 
+C.6-3-65C5x+6-49C5=) 
-C.5+C.3^574C5,-3-65C5=) 
^C^;- 2 -0905.) 

—  C^e -C^j  —  Cj:,— 2-95052— I  •  ISSC53) 

+C=,~C.8+C.5+2-34C5.-o-338C33) 

+  C.6  +  C38+0-6IC5.) 

—  C.4  — 0-2905, +0-29C56—0-29C57) 

+  C\4-C,,  +  2-27C5,-0-058C5,-0-29C5<;+0-29C5,; 

-C\,-C3.-r52C56^r52C5,) 

—  C26— i"98C5,) 
-C30+C3.  +  1-323C53) 
+03,-1-1-52056— 1-52057) 
+  C.6-f-C.,-^03o-I-265053) 

+  03c,-03x-O-480s6+O-48057) 

+03,-1- 1 -28056-1-2805;) 

— 029— 0-80056+0-S0057 ) 

+C.5-030) 

— C30+0-33056— O-33057 ) 

+03=-o-33056+o-33057) 

-03,+o-76056-o-7605,) 

-C3.) 

+  03,+03.-o-76056+o-7605, ) 

-0,6-03,-2-69055-0-3405;) 

+  037^3-03055) 

-0,4-035+036-o-55C54-o-3405s+o-8905;) 

+034+5-84054) 

+  C35-5'29C54-o-55C57) 

-033-034-3-18054+3-1805;) 
+033-035+4-28054-3-1805;) 
+034+035-0,6-1-10054-3-19055) 
+036-038+6-28055-3-0905;) 

+  0,8- 3-O9O55  +  3-O9O57) 

-C38-C35-I-79C5;) 


THR    MAIN    TRIANGULATIOX. 


12" 


-:& 


Conrlalc  equal ioiis  — coiiij)lelc-(l. 


.2 
o 

V. 

5.1UJ 

'0  3J 
V   > 

0 

(121) 

=o-8( 

(122) 

=o-8( 

(123) 

=o-8( 

(124) 

=07  ( 

(125) 

=o-8( 

(126) 

=o-8( 

(127) 

=o-9( 

(128) 

=  i-o( 

(129) 

=o-9( 

(130) 

=o-8( 

(131) 

=o7( 

-C37+C„+r79C57) 

-C36  +  C38  +  0-95C57) 

+036+037-0-95057) 

-C37  +  7-97C55) 

+0,7-035-9-37055-  1-40057) 
+035-040+1-40055-3-32057) 
+040+1-92057) 
-035+040+0-60055) 

-038-3'44C55+3-44C57) 

+038+035+2-84055-3-44057) 

-040-f  I-54C57) 

Normal  eqiialions. 


Ci 

C2 

C3 

C4 

C5 

C6 

C7 

C8 

C9 

Ci3 

Cii 

Ct2 

Cn 

C.4 

C.s 

I 

o=-o-45 

+3-6 

+  1-6 

2 

0=  +0  -46 

+3-6 

-i'7 

3 

o=-o-38 

+4-9 

-1-6 

-1-6 

4 

o=+o  -09 

+5-5 

+  1-6 

+  2-0 

-1-9 

5 

o=-o-o8 

+  5-8 

—  2  -O 

6 

o=— 0-66 

+5-8 

—  I  -S 

7 

o=+o-49 

+5-8 

+  1  8 

4-l-S 

8 

o=+o-07 

+  5-4 

-I  -8 

+  1-8 

9 

0=4-0-85 

+5-4 

+  1-7 

—1-7 

10 

o=+o-09 

+6-4 

-t-7 

II 

o=  — I  -42 

+5-7 

-1-6 

12 

0=i-I  -20 

+5-9 

+  2-0 

4-1  -8 

-I  -s 

13 

0=— 2  -02 

+  5-5 

—  I  '8 

14 

0=  +  I  '22 

-**5  - 

-fS 

Normal  equations— 

-continued. 

C.5 

C,6 

C.7 

C18 

C15     C20    C2, 

C22       C=3 

C24     C25     C25     C27     C28 

C2, 

C3,        C„        C32       C3J 

15 

o  =  +o'39 

-t-5-5 

4-1-8 

-1-9 

-rg 

16 

0=  -f  I  -05 

-t-5-5 

-I-I-7 

-1-7 

-17 

17 

0=4-0 -03 

-I-5-0 

-1-7 

4-1-9   -1-4 

-   ■'7 

18 

o=— o'27 

-(-5-3 

4-2-0              -1-6 

4-1-7     -2-0 

19 

o=+o-6i 

-I-5-6 

—  2-0 

20 

o=-o-23 
0= -1-0 -61 

4-l-s    —1-6 

21 

....       -ri|  J          I  Kj 

-I-4-9 

22 

o=+o-69 

4-5-2    4-1-6 

-1-6 

~    ' 

23 

o=+o-37 

-1-5-4 

-i-S    -1-6 

24 

o=-i-55 

4-5-2                         -1-7 

25 
26 

o=-o-25 
o=— 0-62 

4-5-2                         ~\'^ 

4-5-8    4-1-7    4-2-t 

+  1-7 

27 

o=+o-84 

4-5-2    -1-8 

4-i-S 

4-1-7 

28 

o=+o-o7 

+5-5 

—  rS 

29 

0=4-1-10 

+5-4 

-1-9 

30 

o=  — I  -41 

-t-5-4    -1-8 

+9-0   4-  5'5 

31 

0=4-1-28 

32 

o=— o-ii 

+  144 

128 


THE    EASTERN    OBLIQUE    ARC. 


0=  — I  ■ 

o=  +  i- 
o=  +  i- 

0=+0' 

o=+o  ■ 

0=+0' 
0=+0', 
0=— 0'' 

o=-3-: 
o=-i  • 
o=-i  ■; 

0=— O'i 

o=  +  i  ■■ 
o=-6-: 


Cjq  Ci4 


Nonn.il  t't] nations — continued. 

C36       C37       C38       C59       C40        C41  C4 


C43 


C44 


C46 


+  6-6 


+  1 

■6 

-3 

■3 

+4 

•8 

+  1 

•5 

—  I 

■5 

+  7 

■0 

—  I 
+4 

■5 
•6 

+  i'5 
+4  7 

+5-1 


-1-6 

+  17 
+  5-1 


-1-8 

+3-4 


+51 '123     +1705 
+64-821 


+  0-573 
+78-136 


+     3-95 
—   II 'oo 

+  170 '86 


+     1-36 

-   77-26  +  3-004 

+  185-75  -27  400 

+  54-542 


Norma/  equations — completed. 


C41 

C4C 

C43 

C44 

C45 

C46 

C47             C4f 

C49 

Csc 

C5. 

C5=             C56 

I 

+3-630 

+ 1  -848 

2 

-6  -736 

-5-395 

3 

+6  -043 

+  1  -192 

+6-109 

4 

-I -144 

+5  -426 

-o-oio 

+  1-355 

5 

-I -144 

—  9-662 

+5  -350 

-9-4S0 

6 

+  7-976 

-0-455 

-  4-700 

+  3-929 

7 

-  2  -988 

-  2  -037 

-  0-806 

+  I-20S 

-t-o-So6 

8 

-ho  -208 

-2-990 

+  7-071 

+  1  -20S 

+0  -S80 

9 

+3  -526 

-  S-243 

-2-835 

—  I  -624 

+3  -502 

10 

+o-o8i 

- 1 1  -558 

+5  -084 

- 1  -624 



+0  -44S 

II 

-4  -225 

-2-520 

+2-520 

12 

+0  -462 

-8 -218 

-2-583 

+6-604 

13 

+  I  -066 

+  2-835 

-2-228 

+  2-458 

14 

-4-944 

+  2-106 

-2-583 

-3-132 

Normal  (•(/«<? /'/t';/5— completed. 


C44           C45               C46 

C47 

C4S 

C49 

Cso 

C51 

C5= 

C53 

C54 

C56 

CS7 

15 

+1  -530 

-0  -360 

+0-I4I 

+  I  -406 

+"  ^fig 

16 

-5-659 

—0  -540 

-5  -400 

—  2-222 

+0  -955 

17 

+  1  -021 

+  1  -750 

-I  -822 

—  2-222 

-1-928 

18 

+  0-367 

-2-330 

+3-368 

+  2-503 

—  I  -630 

+  2-528 

-2-604 

19 

+  0-639 

+0-IS6 

-0  -495 

+  I  -630 

-I  -630 

20 

-0  -749 

—  2  '430 

-3-0S0 

+0  -749 

—  I  -320 

21 

+  2-961 

+  1  -728 

+  I  -349 

—  2  -048 

-1-349 

+  2-644 

22 

+0  -367 

+  0-540 

+  5  -400 

+8  -500 

-3  -320 

-2-635 

-0  -436 

23 

—  0-091 

—  0  -911 

-3  -035 

+4  -259 

-3-944 

+5  -436 

24 

+  2-853 

-7-051 

+    I  -827 

+0-213 

+3-190 

-5-530 

25 

-1-448 

-0-777 

+  3-312 

+0  -S48 

26 

—  I -670 

+ 1 2  -S79 

+  0-057 

27 

-I -816 

+   1-548 

+0-133 

+  2-824 

-  2  -824 

28 

+4  -592 

—  0  -29S 

-0-289 

29 

+  0-720 

—0  -480 

-1-584 

+  1  -584 

30 



+   2-655 

+0-525 

—0-480 

+  0-480 

31 

+  1-058 

—0-264 

+0  -264 

32 

-1-672 

+  1-672 

THK    MAIN    TRIANGULATION. 


129 


f 


Noniial  cqualions- 

-completed. 

C47 

C48 

C49                  C5<,                C51 

Cs^-            C5, 

C54 

C55 

Cs'. 

CS7 

33 

-    1-56 

+  6-912 

- 

8  -479 

34 

+  3-2'4 

-      I  -961 

- 

2  152 

35 

-  8-515 

-      1-961 

+ 

IO-I15 

36 

+  0-330 

+     8-S68 

- 

3  042 

37 

-     8-465 

- 

o-8j4 

38 

-     2  -437 

+ 

1-776 

39 

+   10-2S8 

- 

3-485 

40 

—    0-520 

+ 

3  306 

41 

+  II  009 

42 

+  26-SI4 

43 

+     6  -S49 

44 

+     3-3S0 

45 

+  33-633 

46 

+  4  '804 

-   18-595 

47 

0  = 

+0 

■8 

+52  -693 

-  3  76>< 

-  27-64     +  4-307 

-4-096 

48 

0  = 

—  I 

■23 

+  36  •187 

+  32  -60      —  0  -853     +     0  '93 

+     I  -793 

49 

0  = 

-1 

■7 

+  139-92      -10-125     +    9-33 

+  0-450 

+     9-489 

+ 

0-892 

50 

0  = 

+2-4 

+5S72S     -  39-07 

-     I  472 

+ 

3-767 

51 

0  = 

—0 

■7 

+  135-18 

—40-449     —0-106 

-  32 -680 

+ 

32-440 

52 

0  = 

-2 

■0 

+S0-S20     +2-056 

-     5  '261 

+ 

5-261 

53 

0  = 

—0 

■61 

+  7  -56S 

-     2-914 

+ 

2-914 

54 

0  = 

+  1 

•4 

+9S  -900 

+     2-61 

- 

14 -99s 

55 

0= 

—  I 

•0 

+ 194  -42 

- 

56-399 

56 

0  = 

+5  7 

+  171  -07 

- 

52-148 

57 

0= 

+  2 

■6 

+ 

74-110 

C  ,  =+0  -1207 
C  2=  — o  -1272 

C  3=— O  -0699 

C  4  =  -o-32iS 
C5=+o-i829 
C6=+o-33i8 

C  7=— O  -2663 
C8=+0-I052 

Cg=+o-i69S 
Cio=+o-2558 
Ci,  = +0-3849 
C,.= -0-2855 
C,3  =  +o-6S2i 
C,4= +0-0849 

C:5=--0-I424 


Resultius:;  values  of  correlates.. 


Ci6=— o  -2409 
C,./=+o-iSii 
C,i;= +0-4276 
C,5=— 0-3196 

Coo=-Lo  -I91S 

0=,  = +0-1744 
C=.= -0-3624 

C23  =  +0-I242 
C,4  = +0-3096 
C25=— O  -0829 

C,6=+o-2957 
C.;  = -0-1935 

Cj8=— 0-2701 

C;9=— o  -1904 


€30= 

C3.= 

^32  ~ 

C33  = 
C34  = 
C35  = 
C36  = 
C37  = 
C38  = 

c„= 

C4a  = 
C4.= 
C4=  = 
C43  = 


:-rO-i223 
^-0-1395 
=  +0-0363 

: +0-4168 
=  -0-5315 
:— O  -OI9I 

— o  -6061 

:  — O  -2410 
:— O  -2491 
: -0-1599 
=  --0-3927 
+  0  -0652 
:+0  -0481 
: +0-0123 


C44  = 

-0  -0449 

^45  = 

-0  -0375 

C46  = 

-f-o-i3i5 

C47  = 

— 0  0635 

C48  = 

-rO  0569 

C49= 

— 0  0056 

C30  = 

-0-0143 

C3,= 

-0  -0053 

C5=  = 

— 0  0325 

C5.= 

-0  -0530 

C54  = 

— 0  -0247 

C55  = 

—  0  "0236 

Cs6  = 

— 0  0590 

^57  = 

— 00136 

A'esiil/nii;'  corrections  to  directions. 


(i)=  -0-054 

(2)  =  +0-I03 

(3)  =  -fo-36o 
(4)=-o-44i 
(5)  =  -o-oT4 
(6)=:+o-o7o 

(7)  =  +o-o55 

(8)  =  -o-oii 

(9)  =  -o-ii4 
(10)  =  +0-387 

4192 — No.  7 — 02- 


(34)  =  -o-i55 

(35)  =  H  0-303 

(36)  =  -0-304 

(37)  =  --0-603 

(38)  =  -1-0 -294 
(39)=-^-o■356 
■(4o)  =  ^o  -017 

(41)  =  -0-401 

(42)  =-0-044 

(43)  =  -f-o-8oi 


(67)  =+0-228 

(68)  =+o-i26 

(69)  =-0-074 

(70)  =  -0-049 
(7i)  =  --o  -oiS 

(72)  =  — 0-152 

(73)  =  -o-io4 

(74)  =  +o-i36 

(75)  =-0 -002 

(76)  =  -  o-no 


]oo)=-ro  -126 
ioi)=— 0-284 

102)  =  -0-237 

103)  =  — 0-204 

104)  =  — 0-281 

105)  =  — 0-195 
106)=— 0-195 
107)  =—0-262 
ioS)  =  — 0-091 
109)  =  — o  -172 


I30 


THE    EASTERN    OBLIQUE    ARC. 


Resulting  corrections  to  directions — continued. 


(II)= 

— 0 

•270 

(I2)  = 

^0 

■loS 

(13)  = 

— 0 

■199 

(14)  = 

+  0 

■003 

(15)  = 

+0 

•03S 

(i6)  = 

— 0 

•240 

(17)  = 

+0 

■147 

(iS)  = 

+0 

■146 

(19)  = 

— 0 

•202 

(20)  = 

+0 

■027 

(21)  = 

— ^0 

•070 

(22)  = 

— 0 

•025 

(23)  = 

~o 

•212 

(24)  = 

-ho 

•■65 

(25)  = 

^0 

■241 

(26)  = 

— 0 

•106 

(27)  = 

+0 

•130 

(2S)  = 

— 0 

•19S 

(29)  = 

— 0 

•4SS 

(30)  = 

+0 

•769 

(31)  = 

— 0 

•229 

(32)  = 

+0 

•375 

(33)  = 

— 0 

132 

(44)  = 

=  — 0 

■081 

(45)  = 

=  — 0 

•198 

(46)  = 

=  +0 

■104 

(47)  = 

=  — 0 

•404 

(48)  = 

=+0 

•154 

(49)  = 

=+0 

•391 

(50)  = 

=  — 0 

•321 

(51)  = 

=  +0 

■025 

(52)  = 

=  ~o 

■'59 

(53)  = 

=  +0 

•006 

(54)  = 

=  +0 

■112 

(55)  = 

=  -f-0 

•022 

(56)  = 

=  — 0 

•347 

(57)  = 

=+0 

■155 

(58)  = 

=  —0 

■034 

(59)  = 

=+0 

•012 

(60)  = 

=  --0 

•139 

(6i)  = 

=  — 0 

■004 

(62)  = 

=  — 0 

■125 

(63)  = 

=+0 

•347 

(64)  = 

=  — 0 

■080 

(65)  = 

=+0 

•066 

(66)  = 

=  — I 

•16S 

(77) 
(78) 

(79) 
(80) 
(Si) 
(82) 
(83) 
(84) 
(85) 
(86) 

(87) 
(88) 

(89) 
(90) 
(91) 
(92) 
(93) 
(94) 
(95) 
(96) 
(97) 
(98) 
(99) 


Proba])le  error  of  a  resulting  direction  =o"674 


/8^  _ 

V  57    ~ 


=  -0-231 
=  -0-139 
=  +0-137 
=  +0.-026 
=  — o-oo8 

=  -0-525 

=+0-198 
=  +0  -229 
=  —  o  -066 
=  +0-073 
=  +0  -104 
=  -o  -079 

=—0-065 

=  — o  -172 

=+0-394 

=  — o  -187 
=  +0  -006 

=-0-257 

=  +0  -401 
=  +0  -172 

=-0-285 
=-0-153 

=  — o  -026 

±:0"-26. 


(no) 

=  J-o 

•214 

(III) 

=+0 

■281 

(112) 

=  — 0 

■050 

(113) 

=  — 0 

-60S 

(114) 

=+0 

■107 

(115) 

=+0 

-120 

(116) 

=+0 

-299 

(117) 

=+0 

-005 

(iiS) 

=  -0 

•133 

(119) 

=  -0 

•32S 

(120) 

=+0 

-102 

(  '21  ) 

=  — 0 

•084 

(122) 

=  +0 

■275 

('23) 

=  — 0 

-282 

('24) 

=  ~o 

■037 

(125) 

=  — 0 

-127 

(126) 

=  — 0 

•124 

(127) 

=+0 

•330 

(128) 

=+0-247 

(129) 

=+0 

•109 

(130) 

=+0 

•020 

(131) 

=  — 0 

-290 

Rt 

suiting  angles  and  sides 

of  the 

tri 

angulation  between 

the  Epp 

ing  base  net  an 

(/  the  IMassachnsetts 

base: 

also  between  this  base  and  the  Fire  Island  base  net. 

vTo 

stations. 

Observed  angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances. 

Distances 
in  meters. 

0 

/ 

// 

// 

// 

// 

Ragged  Mountain 
•    Humpback 
Mount  Desert 

29 

25 

02  -II 

+0-04 

02  -15 

3-44 

4-761 

268 

0 

57  712-253 

I 

39 

54 

29  -08 

+  0-36 

29-44 

3-44 

4  -.^77 

280 

4 

75  384  -2  2 

no 

40 

38  -68 

+  0-05 

38  73 

3-44 

5-041 

137 

6 

109  935  '4 

Mount  Harris 

40 

32 

25  '22 

+0  -08 

25-30 

3-79 

4-761 

268 

0 

57  7'2-253 

2 

•    Hinnpback 
Mount  Desert 

66 

02 

38-5' 

-0-44 

38-07 

3  -80 

4-909 

249 

6 

81   142  -72 

73 

25 

08  •  1 1 

— 0  TO 

38 -or 

3-79 

4-929 

927 

0 

85  099  -50 

Mount  Harris 

65 

08 

2,T27 

— 0  -02 

37-25 

3-13 

4  -877 

280 

4 

75  384-21 

3 

Mount  Desert 

37 

'5 

30  '57 

+  0-16 

30-73 

3-13 

4  -701 

544 

4 

50  297  -27 

Ragged  Mountain 

77 

36 

o(  -17 

+  0  -24 

01  -41 

i"^i 

4-909 

249 

6 

81    142-72 

Mount  Harris 

105 

41 

02-49 

-F  0  -07 

02  -56 

3-49 

5 -04' 

137 

6 

109  935  -4 

4 

Humpback 

26 

08 

09  '43 

— o-8o 

08-63 

3-48 

4  -70' 

544 

4 

50  297  -27 

Ragged  Mountain 

48 

10 

59  '06 

+0  -20 

59-26 

3-48 

4  -929  927 

0 

85  099-50 

Mount  P.lue 

26 

55 

40  -So 

40-39 

41  -19 

4  -02 

4-701 

544 

4' 

50  297  -27 

5 

IMount  Harris 

94 

22 

34  -42 

-  0-17 

34-25 

4-03 

5-044 

318 

I 

no  743-5 

Ragged  Mountain 

58 

41 

56  94 

-0-31 

56   63 

4  -02 

4-977 

267 

I 

94  900  -20 

THE    MAIN    TRIANGULATION. 


131 


A'l-su/////,!,^  aitffh'x  and  sides  of  the  Iriatiffulalion  behveen  the  Eppinj:;  base 
base;  also  betiucen  this  base  and  the  Fire  Island  base  net 


net  and  the  Massachusetts 
— continued. 


No. 


12 


13 


14 


15 


16 


17 


stations. 

observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
exce.ss. 

Log.  dis- 
tances. 

Distances 
in  meters. 

0 

/ 

// 

// 

// 

// 

Sabattus 

32 

08 

13  -22 

+0  -08 

13  -30 

3-15 

4  -701 

544 

4 

50 

297  27 

Mount  Harri.s 

52 

02 

19  -02 

—0-07 

18  -95 

3-'5 

4-872 

442 

9 

74 

549  ■19 

Ragg;pd  Mountain 

95 

49 

37 '14 

+  0  -07 

37-21 

3-i6 

4-973 

438 

4 

94 

067  -25 

vSabattus 

69 

29 

07  -45 

+0  -38 

07  -83 

5  -09 

4-977 

267 

1 

94 

90f)  •2f) 

Mount  Blue 

6S 

10 

5 1  74 

+  0  -38 

52-12 

5-08 

4-973 

438 

4 

94 

067  25 

Mount  Harris 

42 

20 

15  '40 

—0  -lo 

15-3" 

5  -08 

4  -834  048 

9 

68 

241  -56 

Sabattus 

lOI 

37 

20  '67 

+0-45 

21      12 

4-22 

5-044 

3'8 

I 

no 

743-5 

Mount  Blue 

41 

15 

10-94 

0  'OO 

10-94 

4-21 

4-872 

443 

0 

74 

549  -20 

Ragged  Mountain 

37 

07 

40  -20 

+0  -38 

40-58 

4-21 

4-834 

048 

8 

68 

24'  -55 

Mount  Pleasant 

54 

39 

35  70 

—0  -09 

35-61 

8-II 

5-044 

318 

1 

no 

743  5 

Mount  Blue 

85 

35 

26-05 

—  0  -12 

25-93 

8-IO 

5-131 

493 

6 

135 

361  -0 

Ragged  Mountain 

39 

45 

23 '05 

—  0  -28 

22-77 

8  -10 

4-938 

618 

6 

86  819-76 

Mount  Pleasant 

51 

26 

46  -90 

+  0-24 

47-14 

3-50 

4-834 

048 

9 

68 

241  -56 

Mount  Blue 

44 

20 

15 -II 

—  0    12 

14-99 

3-50 

4  -785 

231 

0 

60 

986  - 1 2 

Sabattus 

84 

13 

08-56 

—  0  -19 

08  -37 

3 '50 

4-938 

61S 

6 

86  819  -76 

Mount  Pleasant 

3 

12 

48  -So 

-0-327 

48  -473 

0-391 

4  -872 

443 

f) 

74 

549  -20 

Sabattus 

174 

09 

30-77 

-0-265 

30-505 

0-392 

5-131 

493 

6 

'35 

361  -0 

Ragged  Mountain 

2 

37 

42-85 

-0  -654 

42-196 

0-391 

4  -785 

23' 

0 

60 

986  ■  1 2 

Mount  Independence 

77 

48 

18  -a 

—  0  -28 

iS-05 

1-94 

4-785 

23' 

0 

60 

986  -12 

Mount  Pleasant 

48 

46 

01  TO 

—0-62 

00-48 

1-94 

4-671 

377 

7 

46 

922-13 

Sabattus 

53 

25 

47 '25 

+  0  -05 

47-30 

I  -95 

4-699 

925 

8 

50 

no  -16 

Mount  Independence 

25 

16 

42-18 

-0-34 

41  -84 

1-83 

4  -834  04S 

9 

68 

241  -56 

Mount  Blue 

17 

04 

28-31 

-0  -35  ^ 

27-96 

1-82 

4-671 

377 

7 

46 

922   13 

Sabattus 

137 

38 

55  -81 

—0-14 

55  -67 

I  -82 

5-032 

067 

2 

107 

663-2 

Mount  Independence 

52 

31 

36 -'5 

-\-  0  -06 

36-21 

3-62 

4  -938 

6:8 

6 

86 

819-76 

Mount  Pleasant 

100 

12 

48  -00 

-0-38 

47-62 

3-62 

5  -032 

067 

2 

107 

663-2 

Mount  Blue 

27 

15 

46-80 

+  0-23 

47-03 

3-62 

4-699 

925 

8 

50 

no-i6 

Mount  Washington 

68 

55 

42-51 

—0  -02 

42-49 

3 '41 

4  -938 

618 

6 

86  819  -76 

Mount  Blue 

30 

23 

02  -89 

3-41 

4-672 

640 

4 

46 

950  -53 

Mount  Pleasant 

80 

41 

25  '33 

-0  -48 

24  -85 

3 -41 

4-962 

918 

5 

91 

S16  -03 

Gunstock 

34 

'9 

40  ■  20 

-1-0  -84 

41  -04 

3  -03 

4-699 

925 

S 

50 

1 10  -16 

Mount  Pleasant 

19 

54 

04  •  38 

+  0  -26 

04  -64 

3-04 

4  -94S  470 

6 

88 

Sn  -79 

Mount  Independence 

53 

46 

22  -53 

+0  -90 

23  -43 

3  -04 

4  -855 

408 

I 

71 

68  r  -66 

Mount  Washington 

58 

41 

21-78 

+0-46 

22  -24 

2-85 

4  -855 

40S 

I 

71 

681  -66 

Mount  Pleasant 

87 

1 1 

42-29 

+o-6o 

42-89 

2-84 

4  -923 

248 

I 

83 

800-79 

Gunstock 

34 

07 

03  -05 

+0  -36 

03-41 

2-85 

4  -672 

640 

4 

46 

950  -53 

THE    EASTERN    OBLIQUE    ARC. 


iS 


^9 


24 


25 


26 


27 


28 


29 


///«!,'■  (DiQ'/t's  aud  sides 

of  the 

triaiii^ulaiioii  bctivccn 

the  Epp 

i/ig'  base  net  anc 

/  the  IMassaeluisetts 

base;  also  betzcech 

tliK 

'  base  am 

/  /he  Fire 

Island  base  net— 

-continued. 

stations. 

Observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances. - 

Distances 
in  meters. 

0 

/ 

// 

// 

// 

// 

Againenticus 

85 

39 

41  '30 

—  0-02 

41  -28 

3-59 

4-948 

470  6 

88 

811  -79 

Gunstock 

48 

29 

43  -Si 

-0-8S 

42-93 

3-59 

4  -824 

135   1 

66 

701  -43 

Mount  Independence 

45 

50 

46  -87 

-0-30 

46-57 

3-60 

4  -805 

515  8 

63 

902  -20 

Aganienticus 

33 

20 

57  -33 

+  0-16 

57-49 

2-78 

4-699 

925  8 

50 

1 10  -16 

Mount  Pleasant 

47 

01 

59  "61 

+  1  -26 

00  -87 

2-79 

4  -824 

135    I 

66 

701  43 

]Mount  Independence 

99 

37 

09-40 

+  0  -60 

10  -00 

2-79 

4-953 

627    I 

89 

872  -56 

Aganienticus 

52 

18 

43 '97 

—  0  -18 

43-79 

3-84 

4  -855  408  I 

71 

68 1  -66 

Gunstock 

82 

49 

24  '01 

—0  -04 

23-97 

3-85 

4  -953 

627  0 

89  S72  -54 

jMount  Pleasant 

44 

52 

0477 

—  I  -00 

03  -77 

3-84 

4  -S05 

515  8 

63 

902  -20 

Unkonoonuc 

53 

00 

53 '60 

+  0  -10 

53-70 

3-25 

4-805 

515  8 

63 

902  -20 

Gunstock 

76 

II 

25-06 

+  0-19 

25  -25 

3-25 

4  -890  346  8 

77 

686  -72 

Agamenticus 

50 

47 

50-46 

+  0-35 

50-81 

3-26 

4-792 

336  4 

61 

992-11 

Thompson 

29 

43 

52-11 

+  0-09 

52  -20 

3-23 

4  -805 

515  8 

63 

902  -20 

Gunstock 

31 

52 

27  -68 

—0  -12 

27-56 

3-23 

4  -832 

776  9 

68 

041  -97 

Agamenticus 

iiS 

2  T 

50  -30 

-0  -36 

49-94 

3-24 

5-054 

430  8 

113 

352  -4 

Thompson 

61 

50 

53  -28 

-0-25 

53-03 

4-13 

4  -890 

346  8 

77 

686-72 

Unkonoonuc 

50 

33 

20-33 

—  0  -09 

20  -24 

4-13 

4  -832 

776  9 

68 

041  -97 

Agamenticus 

67 

35 

59  '84 

-0-71 

59-13 

4-14 

4-910 

955  0 

Si 

461  -99 

Unkonoonuc 

103 

34 

13-93 

-fo  -01 

13-94 

4-15 

5-054 

430  8 

113 

352  -4 

Gunstock 

44 

18 

57  -38 

-1-0-30 

57-68 

4-15 

4-910 

955   I 

81 

462  -00 

Thompson 

32 

07 

01  -17 

~o  -34 

00-83 

4-15 

4-792 

336  5 

61 

992  -13 

Monadnock 

32 

54 

52-43 

4-0-13 

52-56 

I  -93 

4-792 

336  4 

61 

992-11 

Gunstock 

22 

59 

06  -42 

+0  -05 

06-47 

I  -93 

4-648 

835  I 

44 

54S-71 

Unkonoonuc 

124 

06 

06  -72 

+0  -05 

06-77 

;-94 

4-975 

287  4 

94 

468  -59 

Wachusett 

61 

22 

19-44 

-0-17 

19-27 

8  -68 

5-054 

430  8 

113 

352  -4 

Gunstock 

48 

00 

55-09 

—0  -21 

54  -88 

8-68 

4-982 

231  4 

95 

991  -20 

Thompson 

70 

37 

12  -12 

-0-23 

II  -89 

8-68 

5-085 

731  5 

121 

S23  -6 

Wachusett 

57 

33 

20  -78 

+  0-03 

20-81 

4-12 

4  -910 

955  0 

81 

461  -99 

Unkonoonuc 

83 

56 

40-35 

+  0-13 

40 -48 

4-11 

4-982 

231  3 

95 

991  -18 

Thompson 

38 

30 

10-95 

H-Q-Il 

11  -06 

4-12 

4  -778 

830  2 

60 

093  -88 

Wachusett 

3 

48 

58  -66 

—0  -202 

58  -458 

0  -412 

4-792 

336  4 

61 

992-11 

Gunstock 

3 

41 

57-71 

-0-510 

57  -200 

0  -412 

4-778 

830  3 

60 

093  -89 

Unkonoonuc 

172 

29 

05-72 

—0  -142 

04  -578 

0  -412 

5  -085 

731  4 

121 

823-6 

Monadnock 

117 

01 

19-36 

+0-0I 

19  -'37 

3-21 

5-085 

731  4 

121 

823-6 

Gunstock 

19 

17 

08  -71 

-fo-56 

09-27 

3  -22 

4  -654  798  I 

45 

164  -59 

Wachusett 

43 

41 

41  -10 

— o-io 

41  -00 

3-21 

4-975 

287  5 

94 

468  60 

THE    MAIN    TRIANGULATION. 


133 


Ri'sit/liiii^  cuii^/ts  am! 
base; 


sides  of  the  lrian<!;iilation  between  the  Eppirig  base 
also  between  this  Imse  and  the  Fire  Island  base  net — 


net  and  the  Massachusetts 
continued. 


30 


33 


34 


35 


36 


37 


.^S 


39 


40 


41 


Wachusett 
Monad  nock 
Unkonoonuc 

Blue  Hill 

Unkonoonuc 

Thompson 

Blue  Hill 

Wachusett 

Thompson 

Wachusett 
Unkonoonuc 
Blue  Hill 

Beaconpole 
Wachusett 
Blue  Hill 

IManomet 
Blue  Hill 
Thompson 

IManomet 
Beaconpole 
Blue  Hill 

Copecut 

Beaconpole 

IManomet 

Copecut 
Beaconpole 
Blue  Hill 

Copecut 
Blue  Hill 
Manoniet 

Great  Meadow 
Beaconpole 
Blue  Hill 

Great  Meadow 
Blue  Hill 
Copecut 


()l)serve( 

aiijilcs. 

Cont-c- 

tioii. 

Spher- 
ical 

angles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances. 

Distances 
in  meters. 

0 

/ 

// 

// 

f  / 

// 

47 

30 

39  76 

-0  -30 

39  -46 

I  -70 

4  -648 

835 

1 

44  548-71 

84 

06 

26  '93 

—0  -12 

26 -Si 

I  -69 

4  -778 

830 

2 

60 

093  -88 

4<S 

22 

59  -GO 

—0  -19 

58  -81 

I  -69 

4  -654 

798 

I 

45 

'64  -59 

59 

37 

43 '90 

—  0  -29 

43 -6r 

3-74 

4  -9"-> 

955 

f) 

81 

461   99 

35 

14 

58  -03 

-0  -37 

57-66 

3-74 

4-736 

332 

8 

54 

492  01 

«5 

07 

29  -98 

-0  -03 

29-95 

3-74 

4-973 

49' 

2 

94 

078 -6S 

99 

18 

37  -oS 

—  G  -26 

36  -82 

3  -22 

4  -982 

231 

4 

95 

991.  20 

34 

04 

13  '9' 

+  0-03 

13-94 

3-21 

4-736 

332 

6 

54 

49'  -99 

46 

37 

19-03 

-0-I4 

18  -89 

3-22 

4  -849 

420 

I 

70 

70r)  -11 

9' 

37 

34-69 

+0  -06 

34-75 

3-60 

4-973 

491 

2 

94 

078  -68 

48 

41 

42  -32 

+0-50 

42  -82 

3-59 

4  -849 

420 

2 

70 

700-13 

39 

40 

53 'iS 

+0-03 

53 -2 1 

3-59 

4-778 

830 

4 

60 

093-90 

82 

05 

13  -39 

^-o  -66 

14-05 

2-03 

4  -849 

420 

1 

70 

700  ■  1 1 

31 

GO 

49  '40 

+0-17 

49-57 

2  -02 

4  -565 

581 

4 

36 

777  -43 

66 

54 

01  73 

+0-72 

02  -45 

2    02 

4-817 

279 

5 

65 

656  -77 

45 

oS 

44  '^5 

+0  -02 

44 -87 

2-47 

4-736 

332 

7 

54 

492  -(JO 

90 

36 

02  -56 

4-G-20 

02  -76 

2-48 

4  -885 

726 

8 

76 

S64  -67 

44 

15 

19  76 

+  0  -03 

19-79 

2-47 

4-729 

5t3 

> 

53 

643  -(X) 

29 

59 

42-88 

—0-18 

42  -70 

1  -62 

4-565 

581 

4 

36 

777  -43 

46 

49 

04  -89 

—  0  -69 

04  -20 

I  -62 

4-729 

5 '3 

0 

53 

642  -99 

103 

II 

1 8  -63 

-0-66 

17  -97 

1-63 

4  -855 

073 

I 

71 

626  -39 

106 

07 

29-31 

-fo-iS 

29-49 

'■63 

4  -855 

073 

1 

71 

626  -39 

37 

18 

I3'i7 

+0-41 

J3  -58 

1-63 

4-655 

000 

4 

45 

185  -64 

36 

34 

21  -79 

fo-o3 

21  -82 

1-63 

4-647 

629 

9 

44 

425  -26 

41 

5S 

51  '45 

—0  -oi 

51  -44 

I  -37 

4  -565 

581 

4 

36 

777  -43 

84 

07 

1 8  -06 

—0  -28 

17  -78 

I -38 

4  -737 

944 

0 

54 

694  -54 

53 

53 

55-45 

-0-55 

54  -90 

I  -37 

4-647 

630 

0 

44 

425  -27 

64 

oS 

37-86 

+0-19 

38  -05 

I  -88 

4-729 

513 

I 

53 

643  -00 

49 

17 

23-18 

-0  -I  I 

23-07 

t  -88 

4  -655 

000 

3 

45 

185-63 

66 

34 

04  -67 

0-15 

04-52 

I  -88 

4  -737 

944 

I 

54 

694  -55 

69 

09 

39-74 

—0  -qS 

39  -66 

0  -70 

4  -565 

581 

4 

36 

777  -43 

74 

40 

16-66 

-0  -55 

16  -u 

0  -69 

4  -579 

231 

4 

37 

95'  -7' 

36 

10 

06  -84 

-0  -52 

06  -32 

0  -70 

4  -365 

932 

I 

23 

22^  -74 

130 

20 

20  -91 

-0-49 

20  -42 

0-54 

4  -737 

944 

I 

54 

694  -55 

17 

43 

48-61 

—0  -03 

48  -58 

0-53 

4  -339 

491 

3 

21 

852  -01 

31 

55 

53-18 

—0-58 

5-  -60 

^-53 

4-579 

231 

4 

37 

95'   7' 

134 


THE    EASTERN    OBLIQUE    ARC. 


Kcsultin^  angles  and  sides  of  the  triaiigtilalion  between  tlie  lipping  base  net  and  t/ie 
base;  also  betiueen  this  base  and  the  Fire  Island  base  net — completed. 


42 


43 


44 


45 


46 


47 


48 


49 


50 


51 


52 


53 


stations. 

Great  Meadow 

Copecut 

Beaconpole 

r  Massachusett.s  North 
Base 
Great  Meadow 
Beaconpole 

MassachiLsetts  South 

Base 
Beaconpole 
Massachusetts  North 

Ba.se 

Mount  Tom 
Monadnock 
W  chusett 

Bald  Hill 

Monadnock 

Wachusett 

Mount  Tom 
Monadnock 
Bald  Hill 

Bald  Hill 
Mount  Tom 
Wachusett 

Box  Hill 
Mount  Tom 
Bald  Hill 

Ivy 

Bald  Hill 
Box  Hill 

Sandford 
Mount  Tom 
Box  Hill 

Sandford 


Observ'ed  angles 


Correc- 
tions. 


Splier- 

ical 
angles. 


Spher- 
ical 


f  vSan 

]  i^"y 


160 

lO 

9 

70 
58 
51 

Si 
54 

44 

33 
56 


29 
02 

27 

09 

49 
01 

GO 
06 

52 
28 

44 


59  '35 
58  -27 
01  "40 

29  '82 

15  -oi 
17-42 

16  -67 
45 '24 

58  -64 
40-67 
47  "59 


89  46  37 '97 
19  48  48-84 
25-33 


Box  Hill 

Woo.ster 

Ivy 

Sandford 


28 
J32 

95 

28 

55 

75 
62 

42 

65 
33 
80 

14 

34 

130 

31 

34 

114 

74 
56 
49 

53 
47 
78 


05 
05 

52 
39 
27 

16 
24 
19 

43 
25 
50 

48 
47 
24 

27 
16 
15 
02 
21 
35 

47 
40 

31 


49-82 

53 '91 
22  26 

54  78 

43  '62 
J  3 '24 
11-85 

58  -37 
21  -08 

44-95 
02  -79 
46-77 
14-24 

27-49 

43-55 
55-72 

34  -46 
53  -03 
39  -85 

59-13 
51  -65 
14-14 


+0-565  59-915  0-144 
+0-566  58-836  0-143 
+0-279    01-679    0-143 


-0-43 
-0-52 

-0-33 

+0-39 
— o  -20 


+0-18 
+0-04 
+  1  -40 
+0-71 

+0-47 
+0  -16 

— o  -II 

— o  -43 

—0-56 

+0-15 

— o  -29 

-I  -23 
—0-56 

— o  -14 
— o  -26 

— o  -09 

+0-07 

— o  -20 

— o  -09 
— o  "19 

+0-17 
-0-23 

O  -QO 

— o-i8 
— o  -29 

+0-45 

+0  -25 


29-39 
14-49 
17-09 

17  -06 

45-04 


40-85 
47-63 

39  -37 

49-55 
25  -80 
49  -98 

53-80 
21  -83 
54-22 

43-77 
12-95 
10  -62 

57-81 
20-94 
44-69 

02  -70 
46  -84 
14-04 

27  -40 
43-36 

55  -89 

34  -23 
53  -03 
39  67 

59-42 
52  -10 
•4  -39 


0-33 
0-32 
o  -32 

O  -22 
O  -22 


-O  -08  58  -56  O  -22 


2  -62 

2  -61 

2  -62 

1-78 
1-78 
1   -77 

3-29 

3-28 
3-28- 

2-44 

2-45 
2-45 

I  -15 
I  -15 
1  -14 

I  -19 
I  -19 

1  -20 

2  22 
2  -22 

2  -21 

2  -31 
2-31 
2-31 

I  -97 
I  -97 
I  -97 


i^og.  dis- 
tances. 


4  -647  630 
4-365  932 
4  -339  491 

4-365  932 
4-324  757 
4-283  145 

4  -324  757 
4-238  707 

4-178  727 

4-654  798 
4  -835  503 
4-913  165 

4  -654  798 
4-797  545 
4  -995  067 

4  -995  067 

4-678  I  So 
4-913  165 

4-835  503 
4  -797  545 
4  -67S  180 

4  -678  I  So 

4  -459  356 
4-712  792 

4  -459  356 
4  -808  420 

4-933  714 
4-712  792 
4-745  910 
4  -955  070 

4  -808  420 
4-745  910 
4-707  138 

4-707  13S 
4  -669  1 7 1 
4-791  513 


Massaehusetts 


Distances 
in  meters. 


0  44  425  -27 

1  23  223-74 
3  21  852  -QI 

I  23  223  -74 

7  21  123  -10 

5  19  193-12 

7  21  123  -lo 

7  17  326-376 

3  15  091  -32 

I  45  164-59 

I  68  470  -44 

6  81  877-70 

1  45  164-59 

0  62  740  -07 

2  98  870  -61 

2  98  870  -61 

7  47  662-93 

6  8i  877  -70 

1  68  470  -44 
o  62  740  -07 

7  47  662  -93 

7  47  662  -93 

2  28  797  -58 
2  51  616-93 

2  28  797-58 

3  64  331  -00 
3  85  844  -86 

2  51  616-93 

0  55  707  -03 

1  90  171  -67 

3  64  331  -oo 

0  55  707  -03 

1  50  949  -29 


I  50  949  -29 
o  46  684  -31 
4  61  87474 


30  CM.   THFODOLITE. 


I 


75CM.   THEODOLITE. 


THK    MAIN    TRIAXGULATION. 


135 


( 


3.  TKIANGULATION  CONNKCriNC,  TIIK  KIKK  ISLAND  BASK 
NET  WITH  THK  KKNT  ISLAND  HASK  NET  KXTKNDKD, 
CONNECTICUT,  NKW  VOKK,  NKW  JERSEY,  PENNSYL- 
VANIA,    DKLAWARE,      AND     MARYLAND.        1833-1845 

AND   1865. 

The  angular  ineasun;s  of  tliis  section  of  the  (jljHque 
arc  date  from  the  year  1833,  and  were  completed  in  1845. 
The  triangulation  up  to  1843  inclusive  is  essentially  the 
work  of  Superintendent  F.  R.  Hassler.  In  its  composition 
it  reflects  the  custom  in  those  early  days  of  including  but 
a  few  composite  figures,  such  as  quadrilaterals  or  central 
figures,  the  chain  being  made  up  mainly  of  triangles. 
The  number  of  observations  taken  would  now  be  consid- 
ered as  .scanty,  yet  with  the  superior  instruments  Mr. 
Hassler  had  procured,  his  results  reached  a  fair  degree  of 
accuracy.  The  number  of  series,  each  including  a  direct 
and  a  reversed  set,  varied  from  11  to  35,  with  an  average 
of  24.  At  the  six  stations  which  remained  to  be  occupied 
after  his  death  in  November  1843,  the  o1)servations  of  his 
principal  assistant  show  an  extreme  range  in  number  of 
series  between  10  and  73.  The  horizontal  circle  of  the 
theodolite  was  used  at  each  station  in  several  positions, 
most  frequently  in  .six  or  three,  that  is,  by  .shifting  the 
zero  division  of  the  graduation  either  60°  or  120°  for  each 
new  position.  It  was  Mr.  Ha.ssler's  practice  to  observe 
only  at  such  times  as  were  con.sidered  by  him  favorable 
or  conducive  to  good  results.  In  1850-51,  in  the  local  or 
station  adjustments,  the  measures  were  treated  as  directions 
according  to  Bcssel's  method,  and  an  adju.stment  of  the 
triangulation  was  made  in  .sections.  The  results  were 
published  in  the  Coa.st  Survey  Report  for  185 1,  page  222, 
and  following.  Later  on,  in  1866-67,  after  the  reoccupa- 
tion  of  certain  stations  of  the  Fire  Island  base  net,  and 
after  some  revision  of  the  triangulation  about  the  Kent 
Island  base,  a  new  and  more  systematic  adjustment  was 
made,  and  relative  weights  to  the  directions  were  intro- 
duced. These  later  results  were  published  in  the  Coast 
Survey  Report  for  1866,  pages  52-53.  A  discrepancy  of  50 
units  in  the  seventh  place  of  decimals  of  the  logarithm  of 
the  length  was  developed  by  the  triangulation,  and  was 
distributed  in  this  adju.stment  by  a  length  equation.  A 
compari.son  of  these  results  with  the  present  values  of  the 
length  of  the  .starting  line  Bald  Hill  to  West  Hills,  .showed 
a  difference  in  the  logaritlnn  of  4  units  in  the  sevciUh  place, 
whereas  the  new  adju.stment  in  the  vicinity  of  Kent  Lsland 
ba.se  showed  no  di.screpanc\-  on  the  line  Osbornes  Ruin  to 
Turkey  Point.  This  fully  justifieil  the  reteiUion  of  the 
adjustment  of  1866-67,  witli  but  a  .slight  change  due  to  the 


No.  22. 


^ashhua 


'RxiLauvd, 

FireJsl/jTut  ' 
WestJIiUa 


BiLrderi 


Mectingi^use  Hill 
Buch 


Princivio 


Turkey  foint 


Osborrwsjitiiri 


Firaiiy^ 


\ 


Swan  Point 

I    \ 


Tnylor  •xc -^ 

Kilometers 


10      O        10      20      30      40      SO 

Statute  Miles 

10  20  30  M 


136 


THE    EASTERN    OBLIQUE    ARC. 


oradual  dispersion  of  this  small  logarithmic  discrepancy'  of  4  units  in  the  seventh  place 
of  decimals.  The  small  changes  indicated  in  the  angles  of  the  first  and  second  triangles, 
which  do  not  exceed  o"'2 1 ,  and  in  the  last  or  thirtieth  triangle  of  less  than  half  a  second, 
are  due  to  this  method  of  producing  an  accord. 

The  correction  to  the  horizontal  angles  for  height  of  stations  observed  upon  is  less 
than  o"'o2,  and  generalh'  this  need  not  be  considered. 

The  approximate  heights  of  the  stations  are  as  follows: 

Round  Hill 
Harrow  '■'' 
Buttermilk 
Weasel  - 
Beacon  Hill  f 
.Springfield  '^ 
Mount  Rose 
Disborof 
.Stony  Hill  t 
Newtown 
I\Iount  Holly 

The  fact  that  the  spherical  excess  of  the  triangles  was  computed  \vith  reference  to 
the  Be.sselian  spheroid  is  immaterial,  as  the  values  from  the  Clarke  spheroid  would  be 
the  same  within  the  limits  of  the  size  of  the  triangles.  The  details  of  this  adjustment 
have  not  l)een  publi.shed,  and  it  is  de.sirable  to  present  here  certain  leading  quantities, 
l)Ut  it  is  essential  to  bear  in  mind  that  the  1866-67  adjustment  started  from  the  .sides  of 
the  triangle  Tashua,  Ruland,  West  Hills,  as  given,  and  terminated  with  the  .side  Finlay 
to  Pooles  Island.  It  is  therefore  .slightly  longer  than  the  section  which  is  now  under 
consideration.  The  small  corrections  to  the  lines  Bald  Hill  to  West  Hills  and  Csbornes 
Ruin  to  Turkey  Point,  dvie  to  the  readju.stment,  are  not  introduced  here,  but  the  effect 
is  indicated  bj'  the  fractional  seconds  placed  in  parenthesis  and  already  alluded  to  above. 
The  mean  error  of  a  triangle,  derived  from  the  sum  of  the  .squares  of  the  clo.sing  errors, 

V73'g2 
=  zt  i"'50,  and  that  of  an  angle  =h  o"'86,  and  the  probable  error  of  a 

The  probable  error  of  a  direction,  f^,  as  found 


elers. 

Feet 

Meters. 

Feet. 

177 

582 

Willowgrove 

132 

433 

116 

379 

Pine  Hillf 

6r-4 

202 

217 

712 

Yard 

150 

493 

178 

5S3 

Lippincott 

43 

142 

II37 

373 

Bethel 

125 

410 

159 

523 

Burden,  less  than 

500 

1277 

419 

Meetinghouse  Hill 

less  than 

500 

84-2 

276 

Buck,  less  than 

500 

71-6 

235 

Principio,  less  than 

500 

99 

326 

Turkey  Point 

25 

82 

55-3 

181 

Osbornes  Rviin 

90 

295 

33 


direction  eqitals  0^674  — ^ 
n/6 


■41. 


approximately  from  the  individual  measures  at  each  .station,  is  d=o"'25;   hence  the  .square 
of  the  triangle-combination  error  =  tj  =  (o'4i  )'  —  (o'25  )''=  0*107,  which  quantity  was 

I        „,,„_.      Aipi^^  ratio  of  the  greatest  to  the  least  value  of—  is 


added  to  each  f  ^ 
as  o'63  to  o'i2. 


hence 


P 


+v 


p 


^^  Delerniiiied  in  1.S17. 


t  Result  of  spirit  leveliuj; 


THE    MAIN    TRIANGULATIOX. 


137 


Abstracts  of  horizontal  directions  at  the  principal  stations  l>etween  the  Fire  island  and  the  Kent  Island- 
base  nets,  Connecticut,  Nezv  York,  New  Jersey,  Petinsylvania,  Delatvare,  and  Maryland,  /8jj-/Sfs 
and  /S6j. 

Hald  mil,   I'airfield  Count}',  Coiinecticul.     July  23  to  Auj^ust   18,  1.S33.     60'"  direction    theodolite 

Nf).  2.      I',  R.  Ilassler,  observer. 


Num'Der 

of  (iirec-  Objects  observetl. 

tions. 


KcsuUiiifi 
direction  from 
station  adjust- 
ment. 


Approxi- 
mate prot)- 
able  error. 


Keduc- 
lions  to 
sea  level. 


Correc-  Correc- 

-— -  •sii:^  \^,  s<^;ris. 


adjust- 
ment. 


justmeiit 
of  1S66. 


Tashua' 

Kuland* 

8 

West  Hills 

9 

Harrow 

0 

Round  Hill 

O  00 

62  40 

99  31 

121  42 

i.SS  36 


Circle  iTSed  in  VI  positions. 


00  '000 

17  '802 

+"  -056 

40  '''35 
lS'6o9 
54  -002 


o  '60 


-t-o'cx)6 


— O'lOJ 

+  1  '433 


0'27  .... 

o'ly  .... 

0  "40  .... 

Mean  correction 


0"372 


(59 '903) 
(14 -291 J 


-o'2I3  (40-622) 


+o'434 
-0'954 


41-27 
17-65 
53  9 1 


[Vest  Hills,  Suffolk  Count)',  New  York.     Octolier  iS  to  December  r.  rS36.t     75  ""  direction  theodolite 


No.  I.      F.   R.    Hassler,  obser\-er.      Jul}'  18  to  Autju.st    15,  1S65. 
G.  W.  Dean,  olj.server. 


direction  theodolite   No.  i. 


Wooster 

0 

00 

.  00  -000 

±0-06 

-  0  -ooj 

4-0 -169 

(00-166) 

'X)I7 

Azimuth  Mark 

7 

26 

21  -76S 

0-06 

(21-781) 

Tashua t 

21 

35 

06  -476 

0-05 

-1-0  -006 

-0-099 

(06-3S3) 

Sandford 

33 

ss 

36 '531 

o-oS 

-(-0-0I4 

-0  -089 

(36-456) 

Rulandt 

Sg 

14 

44741 

0-32 

+0-226 

(44  967) 

Fire  Island  E;ast  Ba.se  % 

122 

36 

15  '675 

0-33 

— o'40o 

(15-275) 

Fire  Island  West  Basel 

'43 

5S 

00  'SoS 

0-38 

+0-406 

(01-214) 

3 

Harrow  % 

269 

17 

04  •25'' 

o-i6 

+0 

■055 

04-3! 

4 

Round  Hill  t 

331 

59 

49-211 

o'33 

+0 

■314 

49  -52 

5 

Bald  Hint 

359 

21 

01  -916 

0-25 
Meai 

—0  -003 
correction 

-0. 123 

0-013 

(01.790) 

— 0 

log 

01  -Si 

MoiDul  Hill,   Fairfield  Count}-,  Connecticut.     July  5   to   i.S,    1S33. 

F.  R.  Hassler,  observer.;! 


60""  direction  theodolite  No 


Number  of 
directions. 


Objects  obser\'ed. 


Results  from  sta- 
tion adjustment  . 


.-approxi- 
mate proba- 
ble errors. 


Corrections 
from  adju.st- 

nient  of  iS66. 


Final 
seconds 


II 
12 
13 

14 


Bald  Hill 
West  Hills 
Harrow 
Buttermilk  || 


o 

93 
121 
220 


00  -QOO 

,^1^  594 
34  -930 
52  -250 
-3  '560 


±0-25 
0-30 

O  '26 

o  '38 


•  0-275 

—  I  -264 
+0  -965 

-o-iSi 


00  '27 
37  '33 

35  -J-ig 
4^-51 


*The  correction  refers  to  Rulaiid  station  of  1S65.  t  Twenty-six  series  were  ol»ser\'ed  in  1S56. 

I  Hassler,  observer.  ?  Fourteen  series  were  ohser\-ed. 

II  The  reduction  indicated  is  on  observer's  authoritv. 


138 


THE    EASTERN    OBLIQUE    ARC. 


.-l/)s/nuis  of  Iiorizontal  dhcdiouF.  at  the piincipal  stations  between  the  Fire  Island  and  tlie  Kent  Island 
base  nets,  Coiiuecticnt,  Nea'  York,  Neza Jersey,  Pennsylvania,  Delaware,  and  Maryland,  /Sjj-/S^j 
and  /S6j — continued. 

Harnnc,  Queen's  County,  New  York.     November  lo  to  December  12,  1S37.     75 '^'"  direction  theodo 
lite  No.  I.     F.  R.  Hassler,  ob.server.     Twenty-four  series  were  taken. 


Xumlier  of 
directions. 

Objec 

18 

Beacon  Hill 

19 

Springfield 

20 

Weasel  * 

2: 

Buttermilk 

22 

Round  Hill 

23 

Bald  Hill 

24 

West  Hills 

Results  from  sta-  Approxi-  Corrections 

mate  proba-        from  adjust- 


ble  errors. 

ment  of  1S66 

0 

/ 

// 

// 

// 

0 

00 

00  "GOO 

±0-31 

+  0  '060 

32 

08 

GO  764 

0-37 

+0  -438 

54 

02 

55  -302 
-I  -032 

0-24 

—0  -058 

no 

3S 

12742 

0-I7 

-0-133 

128 

21 

16-936 

0  •16 

—0  '071 

U9 

34 

06715 

0.34 

—0  -230 

217 

19 

34  '439 

0-41 

-f  0-213 

Final 
seconds. 


00  '06 

01  '20 

54-21 

12  'Gl 

16-86 
06  -48 
34-65 


Buttermilk,  Westche.ster  County,  New  York.     June  11  to  29,  1833.     ec™  direction  theodolite  No.  2. 
F.  R.  Hassler,  ob.server.     Eleven  .series  were  taken. 


5 

Round  Hill 

6 

Harrow 

7 

Weasel 

0 

00 

fX)  -000 

zhO  -22 

-to  -098 

OO'IO 

63 

46 

44  -026 

0  -22 

4-0 -184 

44-21 

37 

17 

19-193 

0-23 

—0  -291 

18  -90 

Weasel,  Passaic  County,  New  Jersey.     September    19  to  October  23,  1838.     75""  direction  theodolite 
No.  I.     F.  R.  Hassler,  ob.server.     Nineteen  series  were  taken. 


25 

Buttermilk 

26 

Harrow 

27 

Beacon  Hill 

0 

00 

00  -000 

±0  -22 

+0  -235 

oa-23 

49 

54 

10-775 

0  -24 

+0  -loo 

JO  -87 

133 

03 

!  I  -643 

0  "20 

-0-312 

11-33 

Spr2ni;Jield,  Union  County,  New  Jersey.     November  6  to  24,  183S.     75""  direction  theodolite  No.  i. 
F^.  R.  Hassler,  observer.     Twenty  series  were  taken. 


33 

Harrow 

34 

Beacon  Hill 

35 

Mount  Ro.se 

0 

00 

00  -ooo 

±0  -22 

-0  -348 

59-65 

84 

13 

25  -129 

o-j8 

+  0-324 

25-45 

142 

41 

14  -780 

0  -21 

-0-013 

14-77 

Beacon  Hill,  Monmouth  County,  New  Jersey.     July  8  to  24,  1839.     Theodolite  No.  i.     F.  R.  Hassler, 

observer.     Nineteen  .series  were  taken. 


28 

Disboro 

29 

Mount  Rose 

30 

Springfield 

31 

Weasel  f 

32 

Harrow 

0 

00 

00  -ooo 

±0  -21 

-fo-oi6 

00  02 

35 

06 

41  -283 

0  -24 

—0  -091 

41  -19 

108 

40 

25-771 

0  -21 

—  0-267 

25  -50 

129 

30 

52  -007 

0  -20 

+0  -266 

52-27 

172 

19 

04  -232 

0-17 

T-O  -056 

04-29 

*-rhe  correction  is  for  eccentricity. 


t  Angle  between  Weasel  and  Azimuth  Mark,  3°  35'  36"'95±o"-40  . 


THE    MAIN    TRIANGULATIOX. 


139 


Abstracts  0/  horizontal  directions  at  the  principal  stations  between  the  Fire  Island  and  the  Kent  Island 
base  nets,  Connecticut,  New  York,  Nerv  Jersey,  Pennsylvania,  Delaware,  and  Maryland,  /Sjj-/8^f5 
and  /cSY)5 — coiilimieil. 

Disboro,  Mercer    County,   New    Jersey.      August    11    to    28,   1839.     75""  'lireclioii   theodolite    No.   i. 
K.  R.  Hassler,  observer.     Eij<hteen  series  were  taken. 


Numlier  of 
directions. 


36 

37 
38 
39 


objects  observed. 


Stony  Hill 
Mount  Rose 
Springfield 
Beacon  Hill 


Kes\ilts 
tioii  adj 

roiii  sta- 
istmciit. 

Approxi- 
mate proba- 
ble errors. 

Corrections 
•■roni  adjust- 
ment of  1S66. 

0         / 

// 

// 

// 

0     00 

00  '(XX) 

rbO  -22 

-0  -097 

H3     43 

38  -698 

0    16 

-fOII9 

152     47 

13-225 

0-17 

-0-II3 

196     56 

34- 168 

0  '21 

-+-0-085 

Final 
seconds. 


59  90 

3,8  -82 
13-11 
34  25 


Mount  Rose,  Mercer  County,  New  Jersey.     September  29  to  October  17,  1839.     75^'"  direction  theodolite 
No.  I.     F.  R.  Hassler,  observer.     Twenty-one  series  were  taken. 


40 
41 
42 
43 
44 
45 


Springfield 
Beacon  Hill 
Disboro 
Stony  Hill 
Movmt  Holly  ^ 
Newtown 


o  00  00  'ooo 


58  30-192 

38  55  -096 

15  05-181 

146  53  25  -591 

191  24  23  -100 


47 

79 

115 


±0  -20 
o  -20 

0-25 
0-18 

n  -19 

o  -23 


-I-0-016 
— o  -042 
— o  081 
-\-o  -088 

+0  -033 

-o  -033 


00  -02 
30  15 
55 'oi 
05  27 
25-62 
23-07 


Stony  Hill ,   lUirlington   Countj-,   New  Jersey.     September  5  to  24,   1S39.     75'"  direction  theodolite 
No.  I.     F.  R.  Hassler,  observer.     Thirteen  series  were  taken. 


46 

Mount  Holly 

47 

Newtown 

48, 

Mount  Rose 

49 

Disboro 

00  00  -000 

09  51  -295 

35  57  937 

163     16  09  '801 


"3 
102 


=bo  -23 

0  '21 
o  -Jl 
0  -20 


— o  496 
-f  o  -370 
— o  018 
-fo-ii8 


Mount  Holly,  Burlington  County,  New  Jersey.     November  11  to  December  21,  1840.     75' 
theodolite  No.  i.     F.  R.  Hassler,  observer.     Thirt^■-five  series  were  taken. 


59  50 
51 -66 

57  92 
09  -92 

direction 


54 

Pine  Hill 

55 

Yard 

56 

Willovvgrove 

57 

Newtown 

5S 

Mount  Rose 

59 

Stony  Hill 

Nexvlowii, 

Bucks  Couiitv, 

No.  I . 

50 

Mount  Rose 

51 

Stony  Hill 

52 

Mount  Holly 

53 

Willowgrove 

o  <x)  00  -000 

48  51  18-622 

82  09  48  -442 

120  oS  32 -70S 

150  (XI  2  1   -433 

195  46  03    416 


// 
=0-20 
o  22 
0-13 
O  -22 
0-25 
o  -28 


—0-411 
-1-0 -440 

f  o  -244 
—0-669 

-0-218 

-+-0  -665 


59  59 
19  06 
48  69 
32  114 
21  -21 
04  -oS 


Bucks  County,  Pennsylvania.      October  23  to  November  13,  1839.      73'"  direction  theodolite 
F.  R.  Hassler,  oh.server.     Twentv-three  series  were  taken. 


o  CXI  00  000 

62  24  37  -9911 

105  37  14  -249 

180  30  56  392 


d=o  -20 
o  -iS 
o  -20 
0-27 


-to -046 

-o  433 
-ro  -718 

-o  075 


00  05 
37  56 
14-97 
56  02 


♦Angle  between  Azimuth  Mark  and  Mount  Holly.  iii'^^S'  53''-a5±o"-o7. 


140 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directions  at  the  principal  stations  bctiueen  the  Fire  IslaJid  and  the  Kent  Island 
base  nets,  Connecticut,  Neiu  Yoi-k,  Neza  Jersey ,  Pennsylvania,  Delaware,  and  RTaryland,  1833-1845 
and  1S65  -continued. 

Willoicgrove,  Montgomery  County,  Pennsylvania.  November  18  to  December  5,  1839,  and  Novem- 
ber 3,  1840.  75^'"  direction  theodolite  No.  i.  F.  R.  Hassler,  observer.  Thirty-five  series  were 
taken. 


Number  of 
directions. 


Objects  obser\-ed. 


Results  from  .sta- 
tion adjustment. 


Approxi- 
mate proba- 
ble errors. 


Corrections 
from  adjust- 
ment of  1S66. 


Final 
seconds. 


60 
61 

62 


Newtown 
Mount  Holly 
Pine  Hill 


o  00  00  'OOO 
67  07  37  -536 
113     13     31  865 


±0  '20 
OT5 
O  '22 


+  0-279 

— o  '207 
^o  -045 


00  -28 

37  "33 
31  -82 


Pine  Hill .  Gloucester  Count}',  New  Jersey.     October  2  to  December  20,  1842.     75  '"'  direction  theodolite 
No.  1.     F.  R.  Hassler,  observer.     Thirtv-five  series  were  taken. 


63 

Lippincott 

64 

Bethel 

65 

Yard 

66 

Willowgrove 

67 

Mount  Holly  ■■■ 

0 

00 

00  -000 

zbO  -21 

-0  -304 

5970 

24 

t4 

3S  796 

0-I7 

-0  -445 

38-35 

47 

06 

I4-53' 

0-16 

+  0  -329 

14-86 

92 

50 

20-541 

0  -21 

—  0  -026 

20-51 

44 

34 

38-914 
~o  -190 

0-18 

+0  -450 

39  -17 

Yard,  Delaware  County,  Penn.svlvania.  vSeptemljer  26  to  December  i,  1841,  and  August  18  to  Sep- 
tember 12,  1842.  75  '^"'  direction  theodolite  No.  i.  F.  R.  Hassler,  observer.  Thirty-two  series 
were  taken. 


68 

Mount  Holly 

69 

Pine  Hill 

70 

Lippincottt 

71 

Bethel 

o 

00 

00  -OOO 

±o-i6 

—0  -461 

59-54 

33 

40 

iS  -813 

0-13 

-0-257 

18-56 

81 

05 

15-178 

0-15 

+0-521 

15-70 

25 

47 

25  -325 

(J  -26 

-(■0  -262 

25  -59 

Bethel,  Delaware  County,  Pennsylvania.  December  2  to  13,  1843.  75"'"  direction  theodolite  No.  i. 
J.  Ferguson,  observer.  Sixteen  series  were  taken.  May  4  to  8,  1847.  30^'"  repeating  theodolite 
No.  II.     E.  Blunt,  observer.     Thirteen  sets  of  6  repetitions  each. 


72 

Yard 

0 

00        00  -000 

±0  -18 

-0-223 

59-78 

73 

Pine  Hill 

65 

01        53-189 

-  35  -750 

0-23 

+  0-442 

17  -88 

74 

Lippincott 

100 

16      130-880 

0  -26 

—0  -(.)2Q 

49-43 

Lippincott 

0 

-    81  -430 
GO         00  -000 

—  0  -020 

74 

59-98 

75 

Burden 

32 

48         39  -502 
+    47-320 

-0-I35 

86-69 

N.  B.— The 

corrections  are  for  eccentricity. 

*  Direction  corrected  for  eccentricity. 

t-^ngle  between  .\zimutli  Mark  and  I^ippincotl,  167°  00'  o4'"32±o"-22. 


t 


THE    MAIN    TklANGULATIOX. 


141 


* 


ylhslracls  of  horizontal  dircc/ioiis  nl  the  priiiiipu/  sln/io)is  hcliueen  Ihc  Fire  island  and  the  Kent  Island 
l)ase  nets,  Connecticut,  Ne70  York,  Nciv  Jersey,  J'ennsylvania,  Delaware,  and  Maryland,  1833-/8  fs 
and  1865 — continued. 

JJppincott,  Gloucester  County,  New  Jersey.     August  15  to  Septeml)er5,  1843.     75  ""  direction  theodo- 
lite No.   1.      1".  R.  Ilassler,  observer.     Thirty-three  series  were  taken. 


Number  of 

directions. 

objects  ob.ser\ 

76 

Burden 

77 

Meetinghouse  Hill 

7'^ 

Bethel 

79 

Yard 

So 

Pine  Hill 

kt^ulls  from  ela- 
tion a'lj)i^>lmciil. 

Approxi- 
mate proba- 
ble errors. 

Corrections 
from  adjust- 
ment of  1S66. 

c        / 

// 

// 

// 

0     OC) 

CXJ  '(XDO 

±0-33 

-0  472 

73     07 

29  710 

f)  -29 

—  0   296 

117   05 

58-189 

016 

-0  093 

152    06 

60  -223 

0  -22 

-  0  -629 

237     35 

4«  -'"iSS 

(,■26 

-0  ■49<j 

h'iiial 
seconds. 

// 

00-47 

29-41 

58  -28 

59  "59 

49  32 

Burden,''''  Salem  County,  New  Jersey.  September  29  to  November  3,  1843.  75'^'"  direction  theodolite 
No.  I.  F.  R.  Has,sler,  oljserver.  Twenty-six  .series  were  taken.  .Augu.st  22,  1S45.  30""  repeating 
theodoliteNo.il.     K.  Blunt,  observer.      Four  sets. 


f 


81 

Buck 

82 

Meetinghouse  Hill 

^^3 

Bethel 

84 

Lippincott 

0    00 

00  - 000 

=0  -rg 

—  0-146 

59 '^S 

33     22 

27  -846 

016 

-rO-331 

28-18 

72     46 

31  -970 

<'  '33 

+0  039 

32-01 

02     51 

08  -769 

(1  -22 

—0  -256 

oS-5< 

lilectiiighouse  Hill,  Newcastle  County,  Delaware.     September  16  to  26,  1845.     60""  direction  theodc 
lite  No.  2  (regraduated).     J.  Ferguson,  ob.server.     Seventeen  series  were  taken. 


«5 

Lippincott 

86 

Burden 

87 

Buck 

88 

Principio 

O  00  00  -QOO 

37  23  53  -256 

97  15  50-141 

154  '4  56-363 


±0  -27 
o  -30 
o  'iS 
0-44 


—  O  -202 

— o  -501 

-fO-J32 
-t-O-142 


00 

-20 

52 

"75 

50 

■27 

56 

■50 

Buck ,'\  Newcastle  County,  Delaware 
J.  Ferguson, 


July  29  to  August   13,   1845.     60 '^^'"  direction  tlieodolite 
observer.     Seventv-one  series  were  taken. 


No.  2. 


89 

Tuikey  Point 

90 

Principio 

9' 

Meetinghouse  Hill 

92 

Burden 

Deakvne 

0  00  (X)  'OOO 

37  01  12-453 

118  14  25-359 

205  00  00  -673 

248  08  1 1  -297 


ro  -18 
o  -16 
014 
O  '20 
O    21 


+  O-I3I 
—  0-2II 

— o  -101 

-t-0-2II 


CX3 

"  *3 

12 

■24 

25 

■26 

00 

-88 

Principio,  Cecil  County,  IVIaryland. 
J.  Ferguson 


August  17  to  .Septembers,  1845.     60  '"  direction  theodolite 
observer.     Tweiitv-si.K  series  were  taken. 


No.  2. 


93 

Meetinghouse  Hill 

94 

Buck 

95 

Turkey  Point 

96 

Osbornes  Ruin 

0 

00 

00  -000 

==0-25 

-0-159 

59  84 

41 

47 

41   531 

020 

-f  0  -225 

41   76 

119 

25 

09  -985 

0  -16 

+0-089 

10  07 

177 

02 

07  -641 

0  -16 

—0-169 

07-47 

*Last  station  occupied  by  Superintendent  Hassler.     He  died  November  20,  1S4;,. 
t  Also  designated  Buck  j  in  some  records. 


142 


THE    EASTERN   OBLIQUE   ARC. 


Abstracts  of  horizontal  directions  at  the  principal  stations  between  the  Fire  Island  and  the  Kent  Island 
base  nets,  Connecticut,  Neiv  York,  New  Jersey,  Peniisylvania,  Delaware,  and  Alaryland,  jSjj-iS^^ 
and  jS6^ — continued. 

Turkey  Point,  Cecil  County,  Marj-land.     Ma^-  31  to  June  17,  1845.     60'"'  direction  theodolite  No.  2. 
J.  Ferguson,  observer.     Sevent3--three  series  were  taken. 

Correc- 
tion from 
Approx-      adjust-  Correction 


nber  of 
'Ctions. 

Objects  obsen,'ed. 

Results  from  sta- 
tion adjustment. 

imate 

probable 

error. 

ment. 

Special 
Publica- 
tion No. 

Resulting 
seconds. 

from  ad- 
justment of 

1S66. 

Final 
seconds. 

4,  1900. 

0 

/ 

// 

// 

// 

// 

// 

// 

97 

Pooles  Island 

0 

00 

GO  '000 

±0-17 

-r  0  -65 

(00-65) 

—0  -009 

59  "99 

9S 

0.sbornes  Rnin 

44 

or 

48  723 

0  'iS 

-0-44 

(48-28) 

+0-158 

48.  88 

99 

Principio 

131 

U 

41  -244 

o-i8 

—0  -084 

41  -16 

00 

Buck 

196 

36 

01  •'S06 

0  -38 

— O-I18 

or  -69 

Osbornes  A'ui//,  Harford  County,  Maryland.     September  23  to  October  2,  1S44.     60""  direction  theod- 
olite No.  2.     J.  Ferguson,  observer.     Ten  series  were  taken. 


lOI 

Principio 

0 

00 

GO  -000 

d=0  -27 

+0-126 

00-13 

102 

Turkey  Point 

35 

10 

II   -669 

0-39 

4  0-II 

(11-78) 

—0  -268 

II  -40 

103 

Pooles  Island 

116 

37 

29-195 

0-55 

—0-06 

(29-13) 

—0  -461 

28-73 

104 

Finlay 

194 

06 

43  •571 
*44  -955 

0-42 

—0  -09 

(44-87) 

+0-414 

43-98 

Of  the  old  adjtx.stnient  of  1866-67,  retained  here  after  leaving  off  a  few  triangles  at 
both  ends,  -we  shall  onlj-  present  the  observation  equations  and  the  resulting  corrections, 
together  with  the  triangles.  The  following  designations  in  the  old  adjustment  still 
need  explanation;  they  are,  (i),  Ruland  to  Bald  Hill;  (2),  Tashua  to  same;  (6),  Bald 
Hill  to  Tashua,  and  (7),  Bald  Hill  to  Ruland: — at  the  southern  end;  (103)  Osbornes 
Ruin  to  Pooles  Island;  (104),  same  to  Finlay;  (97),  Turkey  Point  to  Pooles  Island; 
(105),  (106),  (107),  Pooles  Lsland  to  Finlay,  Osbornes  Ruin,  and  Turkey  Point, 
respectively. 


I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 


o=^i-525-(6)  +  (7)-(i)  +  (2) 

o=-fi-433--(7)  +  (8)-(5)  +  (i) 
o=+2-4S3-(ii)  +  (i2)-(4)  +  (5)--(8)  +  (io) 
o=-i-397-(ii)  +  (i3)-(22)  +  (23)-(9)  +  (io) 

0=-2-77I-(22)  +  (24)-(3)  +  (4)-(l2)+(l3) 

o=+o-996--(i5)  +  (i6)-(2i)  +  (22)-(  13)^(14) 
o=+o-686-(25)  +  (26) -(2o)  +  (2i)-(  16)4(17) 
o=+o74i-(3i)+(32)-(i8)  +  (2o)-(26)+(27) 

o=-i-372-(33)  +  {34)-(3o)+(32)-(i8)+(i9) 
o=+o-57i-(4o)  +  (4i)-(29)  +  (3o)-(34)  +  (35) 
o=+o-i79-(37)-L(39)_(28)  +  {29)  -(41)  -!-(42) 
o=-o-522  -(48)  +  (49)-(36)  +  (37)--(42)-|  (43) 
o=-i-3o6-(58)  +  (59)-(46)+(48)-(43)  +  (44) 


*  See  result  of  the  measures  of  iSgfi   Coast  and  Geodetic  Survey  Special  Publication,  No.  4,  p.  354. 


THK    MAIN    TRIANGULATIOX. 


143 


XIV 

XV 

XVI 

XVII 

XVIII 

XIX 

XX 

XXI 

XXII 

XXIII 

XXIV 

XXV 

XXVI 

XXVII 

XXVIII 

XXXIX 

XXX 

XXXI 

XXXII 
XXXIII 
XXXIV 

XXXV 


o=-i-o57-(5o)H  (52)--(57)+(5S)-(44)^-(45) 
o=-3-35'"-{57)  !  (59)-(46)  +  (47)  (sO-fSz) 
o=-|-2-493-(6oj  +  (6i)  (56)1(57)  (52)  '(53) 
o=~r294-(66)-|  (67)^-(54)H-(56)-(6i)  j  (62) 
o=_i-i76-(6S)  +  (69)-^  (65)  +  (67)  -(54)-'-(55) 
o=-i-959-(72)-|-(73)-(64)  ■  (65)  (69)  •  (71) 
o=--2-57o-(79)-K8o)-(53)-|  (65)-~(69)  i  (70) 
o=+078o-(72)  +  (74)-(78)  i-(79)  (70)  h(7i) 
o=^-o■7S9-(83)^(84)-(76).1-(7S)-  (74)  ■  (75) 
o=  +  2-o59-(85)+(86)--(82)  +  (84)-(76)  +  (77) 
o=-I•422-(9I)  +  (92)-(8I)^  (82)  -(86)  +  (87) 
o=-o-503-(93)  +  (94)-(9o)+(9i)^(S7)4-(88) 
o=-|o-5ir-(99)  +  (ioo)-(89)-H(9o)-(94)  +  (95) 
o=+o•895-(IOI)^  (io2)-(98)  +  (99)-(95)-f-(96) 
o=+o-o72  — (106)4(107)  (97)-i-(98)-(  102)4- (103) 
o=— 2'098—  (io8)H-  (106)  — ( 103)+  (104) 

o=+o-3i25o+o-i44i5(6)  -o-03534(8)-o-55583(  i)  +o-5i5o6(5)-o-ioSS[  (7) 
o=— o-i9647-o-5i563(4)  1  0-40701(5)  t  o'53867(22)+o-oo378(24)— o-2So33(9)--o-i5426i  10) 
+o-i26o7(8)+o-io862(3)— 0-54245(23) 


o=— 0-03765— 0-29742(38)  +0 
+o- 13328(30)— 0-07116(28 

0=:+0-29283— 0-36253(47) +0 

+0-16225(45)  +0-05189(43 

o=+o-i5673— 0-40626  (70)  +0 
+0-33601  (74)-o-o38i9(72 


o=+o-5oi23+o-i3036(2)+o-ioS62(4)— 0-10862(3)  —0-03534(6)  — o-09074(8)-ro-i26oS(  lo) 


+0-01310(12)— 0-013 io(  II 
-o-33522(i8)+o-33522(i9 
+0-17729(25) +0-02529  (27 
+  0-02 130  (33) -0-1505 1  (34 
+0-21414(45) +0-09031  (39 
+0-04706(46)  +0-20502(58; 
+0-00204(52 )  +0-05683  (53 
HO- 16605(66) -I- 0-46753(64 
—0-09809(73)4-0-09809(72 
-o-o6387(76)+o-o6387(77 
+0-27541  (85) -0-2754 1  (86 
+0-27921(90)— 0-27921(89 


21685(39)  +0- 15 129(40)  -t-o-o3S46  (42 )  -0-062 1 2 1 29) 

o-oSo57(37)-o-iS975(4i) 
25601  (48) +0-31275(57) +0-05396(59) -0-21414(44  I 
+0-10652(46)- 0-36671(58) 

21275(71)4-0-27191(63)  1-0-19563(65) -0-29782(73) 
+0-19351  (69)-o-46754(64) 


+0-03148(13) -0-03148  (14) -0-00378(24) +0-00378(22) 
-!-o-io37o(  15)-  oi66o3(  i6)+o-o6233(i7)— 0-20258(26) 
-0-22735(32 ) -i  0-22735(31 ) -j-o-29946( 29) -o-29946( 28) 
+0-12921(35)  o-iS975(4i)+o-iS975(4o) -0-21414(44) 
—0-06716(37)— 0-02315(36) +0-07124(48)— 0-11830(49) 
-0-20502(59) -o- 18397(54) +o-iS397(55)-o-o5887(5o) 
—0-29146  (61) +0-08883(60) +0-20263(62)— 0-16605(67) 
-0-46753(63) +o-3i6ci4(6S) -0-30825(69) -0-00779(71) 
-0-32641  (74) -Uo-3264i( 75) +0-12401  (80) -0-12401(78) 
t  0-36356(83) ~o-36356(84)+o-3i962(82) -0-31962 (Si) 
—o- 13681(87) +0-13681  (88)— 0-01192(92)— 0-01192(91) 
+0-23553(93) -0-23553(94) -0-13354(95)^-0- 13354(96) 
— o-o966o(  100)  fo-0966o(99)+o-2i78o(9S)— 0-21780(97)  -!-o-298Si(  loi)  -o-298Si(  102) 
— 0-04673  (103) +0-04673  (104)— 0-15010  (107 1-1-0- 15010(106) -'-o-i89i9(  10SI 


144 


THE    EASTERN    OBLIQUE    ARC. 


It  will  not  be  necessary  to  transcribe  here  the  correlate  and  normal  eqtiations,  since 
the  resulting  triangles  given  ftirther  on  prove  the  correctness  of  the  solution.  The 
individual  corrections  to  the  directions,  together  with  their  assigned  weights,  are  as 
follows: 


Correc- 

Reciprocal of 

Correc- 

Reciprocal of 

Correc- 

Reciprocal of 

tion 
symbol. 

weight,   -r 

Correction. 
// 

tion 
symbol. 

weight,   -r 

Correction. 
// 

tion 
symbol. 

weight,   -T 

Correction 
// 

(I) 

0  ■  I  So 

+  0  -04S 

(38) 

0-136 

-0-II3 

(74) 

0-175 

-0  -020 

(2) 

0  -301 

-0-413 

(39) 

0-151 

+  0  -085 

(75) 

0-129 

-0-135 

(3) 

"■133 

+  0  -055 

(40) 

0-147 

4-0  -016 

(76) 

0  -216 

+  0-472 

(4) 

n  -216 

+0-314 

(41) 

0-147 

—0  -042 

(77) 

0  -191 

—  0  -296 

(5) 

I )  •  1 70 

— 0  -109 

(42) 

0  - 1 69 

—0  -oSi 

(78) 

0-133 

+  0  -093 

(6) 

o'J55 

-f  0  -039 

(43) 

0-139 

+0  -0S8 

(79) 

0-155 

—  0  -629 

(7) 

0  -467 

+  2-024 

(44) 

0  -143 

+0  -033 

(80) 

0  -iSo 

+  0  -490 

(8) 

0  •  1  So 

+  0  -434 

(45) 

0  -160 

—0  -033 

(81) 

0-143 

—  0  -146 

(9) 

"•143 

-0-954 

(46) 

0  -160 

—0  -496 

(82) 

0-133 

+0-33' 

(lo) 

0  -267 

—  0  -0S7 

(47) 

0-151 

+0  -370 

(83) 

0  -216 

+0  -039 

(II) 

0  '169 

4o  -275 

(48) 

0  -JI9 

— 0  -orS 

(84) 

0-155 

—  0-256 

(12) 

0-197 

—  I  -264 

(49) 

0-147 

+0-II8 

(^5) 

0  -iSo 

+  0  -202. 

(13) 

o'i75 

+0  -965 

(50) 

0-147 

+  0  -046 

(^6) 

0-197 

-0-501 

(14) 

0-251 

—0  -iSi 

(51) 

0-139 

-0  -433 

(87) 

0-139 

+  0-132 

(15) 

"•155 

+0  -09S 

(52) 

■      0-I47 

+0-718 

(88) 

0-301 

+  0-142 

(i6) 

"•155 

+0-1S4 

(53) 

0  -180 

-0-375 

(89) 

0-139 

+  0-131 

(17) 

0  - 1 60 

—0  -291 

(54) 

0-147 

—0  -41 1 

(90) 

0133 

—  0  -211 

(IS) 

0  -203 

+0  -060 

(55) 

0-155 

+0  -440 

(91) 

0  -127 

~o-ioi 

(19) 

0  -244 

+0  -438 

(56) 

0-124 

+0  -244 

(92) 

0-147 

+  0-2II 

(20) 

0-165 

—0  -058 

(57) 

0-I55 

—0  -669 

(93) 

0  -167 

-0-159 

(21) 

0-136 

-0-133 

(58) 

0-169 

— 0-21S 

(94) 

0-147 

+  0-225 

(22) 

o-:33 

—0  -071 

(59) 

0-185 

+0  -665 

(95) 

0-136 

+  0  -089 

(23) 

0  -229 

—o  -230 

(60) 

0-147 

+0-279 

(96) 

0-136 

—  0-169 

(24) 

0-275 

+0-213 

(61) 

0  - 1 29 

—0  -207 

(97) 

0-136 

—  0  -009 

(25) 

0-155 

+  0-235 

(62) 

0-155 

—0  -045 

(98) 

0-139 

+  0-158 

(26) 

0-165 

+0  -]oo 

(63) 

0-151 

-0  -343 

(99) 

0-139 

—  0  -0S4 

(27) 

0-147 

—0  -312 

(64) 

0-136 

~o  -445 

( 100) 

0-251 

-O-I18 

(28) 

0-151 

+0  -016 

(65) 

0-136 

+0  -329 

(lOl) 

o'lSo 

+0-126 

(29) 

0-165 

—0  -091 

(66) 

0-151 

—0  -026 

(102) 

0-259 

-0  -268 

(30) 

0-151 

—0  -267 

(67) 

0-139 

+0  -450 

(>o3) 

0-409 

—  0  -461 

(31) 

0  147 

+0  -266 

(68) 

0-133 

—0  -461 

(104) 

0-283 

+  0-414 

(32) 

0-136 

+0  -056 

(69) 

0  - 1 24 

-0  -257 

('05) 

(33) 

0-155 

-0  -348 

(70) 

0-129 

+0-521 

(106) 

0  -124 

+  0-I24 

(34) 

0-139 

+0  -324 

(71) 

0-175 

+0  -262 

(107) 

0-147 

+  0-077 

(35) 

0-151 

-  0  -013 

(72) 

0-139 

-0-223 

(loS) 

0-625 

—  I  -ICO 

(36) 

0-155 

-0  -097 

(73) 

0-160 

+0  -442 

(109) 

(37) 

0-133 

+  0  - II 9 

Vi6-7  " 
=  ±0  "47 


Resulting  angles  and 


\ 


No.  Stal 

Round  Hill 
Bald  Hill 

West  Hill.s 

Harrow 
Bald  Hill 

West  Hills 

I   Harrow 
Round  Hill 
West  Hills 

I  Harrow 
Round  Hill 
Bald  Hill 

IButterniilk 
Round  Hill 
Harrow 

I  Weasel 
Buttermilk 
Harrow 

I  Beacon  Hill 
Weasel 
Harrow 

{Springfield 
Harrow 
Beacon  Hill 

f  ]Mount  Rose 
9  I    Springfield 
[  Beacon  Hill 

IDisboro 
Springfield 
Beacon  Hill 

IDisboro 
jNIount  Rose 
Beacon  Hill 


4192 — No.  7 — 02 


THE 

:  M 

AIN   T] 

RIANGU 

LATIC 

)N. 

145 

s  of  11  u-  hi  an 

ijHlation 

between  the  Fin 

Island  base  net 

and  the  extended 

)ict 

^f  the  Kent  Island  base. 

Observed  aiiKles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

I.oj;.  dis- 
tances. 

iJistances  in 
meters. 

0 

/ 

// 

// 

// 

// 

93 

33 

38  '59 

-I  -54 

37-05 

0-66 

4-648 

135  6 

44 

477  -oi 

59 

<'5 

'3 ''7 

(■38) 

-0-52 

.2-65 

0-66 

4  -582 

434  I 

38 

232  62 

27 

21 

12  70 

(  -58) 

—0-42 

12-28 

0-66 

4-311 

236  3 

20 

475  -58 

67 

45 

2772 

+0-45 

28 -17 

0-68 

4  -648 

135  6 

44 

477  -01 

22 

10 

37  77 
(  -58) 

-I  -39 

36  -38 

0-68 

4  -258 

590  2 

18 

138  -03 

90 

03 

57  "65 

(•54) 

—0  -16 

57  -49 

0-68 

4-681 

716  2 

48 

052  -52 

SS 

5S 

17-50 

+0-28 

17-78 

0-52 

4-582 

434   1 

38 

232  -63 

28 

18 

56-34 

+  2-23 

58  -57 

0-52 

4  -258 

590  2 

18 

138  -03 

62 

42 

44-95 

-ro  -26 

45  21 

0  -52 

4-53' 

267  4 

33 

983  -45 

21 

12 

49  -78 

—0  -16 

49-62 

0  -50 

4-311 

236  3 

20 

475  -58 

121 

52 

34-93 

+0-69 

35-62 

0-50 

4-681 

716  2 

48 

052  -52 

36 

54 

35-39 

+0-87 

36-26 

0-50 

4-531 

267  4 

33 

983  -45 

63 

46 

44-03 

-fo-09 

44-12 

0-33 

4-531 

267  4 

33 

983  -45 

98 

30 

13-76 

-I -15 

12  -61 

0-33 

4  573 

62S  3 

37 

465  -22 

17 

43 

04-19 

+0  -06 

04-25 

0-32 

4  -061 

771   2 

II 

5  28  -46 

49 

54 

10  78 

-0-14 

10-64 

1-24 

4-573 

62S  3 

37 

465  -22 

73 

30 

35-17 

—0-48 

34-69 

I  -24 

4-671 

752  6 

46  962  -65 

.56 

35 

18-47 

—0-07 

iS  -40 

I  -25 

4-611 

542  6 

40 

S82  -98 

42 

48 

12  -22 

—  0  -21 

12  -01 

2  -20 

4-671 

752  6 

46  962  65 

S3 

09 

GO  '87 

-0-41 

00  -46 

2  -21 

4  -836  466  7 

68  622  -52 

54 

02 

54-27 

—0  -12 

54-15 

2  -21 

4-747 

798  S 

55 

949 -84 

84 

'3 

25-13 

+  0  -67 

25  -80 

1  -91 

4  -836 

466  7 

68  622  -52 

32 

08 

00  76 

+  0-38 

01  -14 

I  -91 

4-564  498  I 

36 

685  -Si 

63 

38 

38  -46 

+0-32 

38 -78 

I  -90 

4-791 

(X19  9 

61 

803-04 

47 

58 

30-19 

—0  -06 

30-13 

1  -25 

4-564  498  I 

36  685  -Si 

5S 

27 

49-65 

-0-34 

49-31 

1  -25 

4-624 

192  9 

42 

09'  -36 

73 

33 

44-49 

— o-i8 

44-31 

1  -25 

4-675 

473  3 

47 

366  -72 

44 

09 

20-94 

-f  0  -20 

21  -14 

071 

4  -564  498  I 

36  6S5  -81 

27 

TO 

15  -49 

0  -70 

4-381 

0S6  I 

24  04S  39 

loS 

40 

25  -77 

—0  -28 

25  -49 

0-71 

4-698 

022  4 

49  891  02 

U3 

12 

55  -47 

—0  -03 

55  -44 

0-50 

4-624 

192  8 

42 

091  -35 

31 

40 

24  90 

— 0  -03 

24  -87 

0-49 

4  -381 

»>86  I 

24  04S  -39 

35 

ID 

06 

41  -28 

— o-ii 

41-17 

0-49 

4  -420  656  6 

26 

342  48 

146 


THE    EASTERN   OBLIQUE    ARC. 


Result  ins:  ans'lcs  and  side 


of  the  triangulation  betzveen  the  Fire  Island 
net  of  the  Kent  Island  base — continued. 


base  net  and  the  extended 


14 


15 


16 


17 


18 


19 


23 


stations. 

Ob.se  rvec 

angles. 

Correc- 
tion. 

ical 
angles. 

.^pner- 

ical 
excess. 

Log.  Dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

/' 

Disboro 

69 

03 

34  '53 

-0.-23 

34  -30 

I  -04 

4-675 

473 

2 

47  366-71 

Mount  Rose 

79 

38 

55"  10 

— OTO 

55-00 

I  -04 

4-698 

022 

4 

49   891  -02 

Springfielil 

3t 

17 

33  -82 

r  -04 

4-420 

656 

6 

26   342  -48 

vStony  Hill 

60 

40 

1 1  -86 

1   0-14 

12  -QO 

0-39 

4-420 

656 

6 

26   342  -48 

Mount  Ro.se 

35 

36 

10  'oS 

-\  0  -17 

10-25 

o'39 

4-245 

277 

5 

17    590-47 

DLsboro 

83 

43 

3870 

-i-O  -22 

38  -92 

0-39 

4-477 

626 

0 

30  034  -89 

Mount  Holly 

45 

45 

41-98 

4-0  -88 

42  -86 

0-54 

4-477 

626 

0 

30  034  -89 

Mount  Rose 

3' 

38 

20  -41 

-0  -05 

20-36 

0-55 

4  -342 

240 

8 

21    990-79 

Stony  Hill 

102 

35 

57-94 

+0  -48 

58  -42 

0-55 

4  -611 

856 

8 

40   912  -58 

Newtown 

4! 

12 

36  -26 

+  I-I5 

37 '41 

0-54 

4-342 

240 

8 

21    990-79 

Stony  Hill 

63 

09 

51  -29 

+0-87 

52  -16 

0-53 

4-473 

984 

7 

29    784-12 

Mount  Holly 

75 

37 

30-71 

+  1  '33 

32-04 

o-,54 

4  -509 

657 

7 

32  333  -87 

Newtown 

105 

37 

14-25 

4-  0  -67 

14  -92 

0-51 

4  -611 

856 

8 

40  912  -58 

Mount  Rose 

44 

30 

57-51 

—0-07 

57-44 

0-51 

4-473 

984 

7 

29  784-12 

Mount  Holly 

29 

51 

48-72 

4-0  -45 

49 '17 

0-51 

4  -325 

374 

2 

21   153-11 

Newtown 

64 

24 

37-99 

—0  -48 

37-51 

0-52 

4-477 

625 

9 

30  034  -88 

Mount  Ro.se 

76 

09 

17-92 

—  0  '12 

17  -80 

0-52 

4-509 

657 

7 

32  333  "87 

Stony  Hill 

39 

26 

06  -64 

-0-39 

06-25 

0-52 

4  -325 

374 

2 

21   153-11 

Willowgrove 

67 

07 

37-54 

-0-49 

37-05 

0-48 

4  -473 

984 

7 

29  784-12 

Newtown 

74 

53 

42-14 

—  I  -10 

41  -04 

0-48 

4-494 

280 

7 

3 1  209  -06 

Mount  Holly 

37 

58 

44-27 

—  0  -91 

43  -36 

0-49 

4  -298  685 

8 

19  S92  -33 

Pine  Hill 

51 

44 

1S-18 

4-0  -48 

18-66 

0-75 

4-494 

280 

7 

3 1  209  -06 

Willowgrove 

46 

05 

54-33 

+0-16 

54-49 

0-75 

4-456 

957 

7 

28  638  -99 

Mount  Holly 

82 

09 

48  -44 

+0-66 

49-10 

0-75 

4  -595 

230 

7 

39  375  -92 

Yard 

33 

40 

18  -81 

+0  -20 

19-01 

0-93 

4  -456 

957 

7 

28  638  -99 

Mount  Holly 

48 

51 

18  -62 

1  0  -85 

=9-47 

0-94 

4  -589 

931 

4 

38  898  -37 

Pine  Hill 

97 

28 

24-19 

+  0  -12 

24-31 

0-93 

4  -709  403 

7 

51  215-76 

Lippincott 

85 

28 

48  -61 

+  I-I2 

49-73 

0  -69 

4  -589 

931 

4 

38  89S  -37 

Yard 

47 

24 

56  -37 

+  0  -78 

57-15 

0  -70 

4  -458  328 

4 

28  729-52 

Pine  Hill 

47 

06 

14-53 

+  0  -67 

15  -20 

0  -69 

4-456 

145 

5 

28  585  -48 

Bethel 

35 

15 

32-01 

—  0  -46 

31  '.55 

0-43 

4  -458  328 

4 

28  729 '52 

Pine  Hill 

24 

14 

38  -80 

-Q-IO 

38-70 

0-43 

4-310 

393 

7 

20  435  -90 

Lippincott 

120 

29 

50-65 

+  0-39 

51  -04 

0-43 

4  -632 

282 

7 

42  S82  -76 

Bethel 

100 

16 

49  "45 

-|-0  "20 

49  '65 

0-28 

4  -456 

145 

5 

28  585  -48 

Yard 

44 

42 

10-15 

—0-26 

09-89 

0  -29 

4-310 

393 

7 

20  435  -90 

Li])pincott 

35 

01 

02-03 

-0-72 

01  -31 

0-28 

4-221 

948 

9 

16  670  -51 

THE 

MAIN    TB 

JANGULATIO 

N. 

147 

Res 

tdtin_s;  angles  ami  sides 

of  Ihe  li-iaiig 

Illation   lyetiueen  11 

e  /'ire 

/stand  Itase  net  ana 

'  the  ex 

■tended 

net  of 

Ihe 

k'eiit  Island  l>ase — 

continued. 

No. 

stations. 

()l>serve( 

aiiKles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Ix>g.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

'  Bethel 

65 

01 

17-44 

-|c)  -67 

18-11 

0  -55 

4-589  93' 

4 

38  898  -37 

24   . 

Yard 

92 

07 

06-51 

{  0  -52 

07  -03 

"•55 

4  -632    282 

6 

42 

882  -75 

Pine  Hill 

22 

51 

35  '74 

-fo-77 

36  -5  1 

0-55 

4-221    94M 

9 

;6 

670-51 

Burden 

30 

04 

36  -80 

—0  -30 

36  -5') 

0-34 

4-310  393 

6 

20 

435  -89 

25 

Bethel 

32 

49 

26-82 

—0  -I  r 

26  -71 

0  -34 

4  -344  465 

5 

22 

103  -73 

Lippincott 

117 

05 

58-19 

-  0-3S 

57  ■■^' 

0-34 

4-559  9'4 

6 

36 

3or)  -67 

'  Meetinghouse  Hill 

37 

23 

53  -26 

—0  •70 

52  -56 

0  -61 

4  -344  465 

5 

22 

'03  -73 

26 

Lippincott 

73 

07 

29-71 

-0-77 

28  -94 

0  -61 

4-541  914 

f) 

34 

826  -V, 

^  Burden 

69 

28 

40-92 

-0-59 

40  -33 

0  -61 

4-532  554 

6 

34 

084  -32 

'  Buck 

86 

45 

35-31 

+0-31 

35-62 

0  -49 

4-541  913 

9 

34 

.S26  -82 

27   . 

Meetinghouse  Hill 

59 

5' 

56  -89 

+0-63 

57-52 

0-49 

4  -479  550 

7 

30 

168  -29 

Burden 

33 

22 

27-S5 

+0  -48 

28  -33 

0-49 

4  -283  056 

5 

19 

189   iS 

Principio 

41 

47 

41  -53 

+0  -38 

41  -91 

0  •3« 

4  -283  056 

5 

'9 

1S9-18 

28 

Meetinghouse  Hill 

56 

59 

06  -22 

-fo-oi 

06-23 

0-39 

4-382  796 

0 

24 

143  -27 

Ruck 

Si 

13 

12  -91 

+0  -11 

13-02 

0-39 

4-454   159 

6 

2,S 

455-06 

Turkey  Point 

65 

21 

20-56 

—0-03 

20-53 

0  -32 

4-382  796 

0 

24 

143  -27 

29 

Principio 

77 

37 

28  -45 

-0-14 

28-31 

0-32 

4-414  063 

I 

25 

945  56 

Buck 

37 

01 

12-45 

-0  -34 

12   12 

0-32 

4-203  937 

I 

15 

993  26 

30 

Osbornes  Ruin 
Principio 

35 

57 

10 
36 

II  -67 

(II -78) 
57-66 

—0  -40 
—0  -26 

II  -27 
57-40 

0-31 
0  -32 

4  -203  937 
4-370  101 

r 
8 

15 
25 

995  26 

447  -78 

Turkey  Point 

a? 

12 

52-52 

(52  -96) 

-0-24 

52  -28 

0-32 

4  -443  000 

9 

27 

733  -26 

148 


THE    EASTERN    OBLIQUE    ARC. 


No.  23. 


iJfump  b  CLC  Tc 


Spt 


'Tobi 


I  Row 


.ong 


kFlat  Top 


Smith  Mt. 


(BuJFaZo 


Moore^ 
Kilometers 


o  10  20         30 

Statute  Miles 


j-l   i-i   i-i-ca- 


4.  FIRST  SECTION  OF  THE  TRIANGULATION,  SOUTH 
OF  THE  TRANSCONTINENTAL  TRIANGULATION, 
IN  VIRGINIA  AND  NORTH  CAROLINA,  1875- 
1879. 

In  connection  with  the  account  of  the  Kent 
Island  base  net  and  its  extension  to  the  westward 
there  are  given  the  abstracts  of  the  horizontal  direc- 
tions as  well  as  the  adjusted  angles  and  triangle 
sides  between  the  triangulation  stations  which 
connect  that  base  with  the  sides  of  the  triangle 
Humpback,  Tobacco  Row,  Spear.  It  is  from  this 
triangle  that  the  triangulation  of  the  oblique  arc 
departs  from  that  of  the  arc  of  the  parallel  and  the 
first  section,  proceeding  to  the  southward  and  west- 
ward, terminates  at  the  line  Buffalo  to  Moore. 
Between  Humpback  and  Moore  the  triangulation  is 
so  strengthened  by  the  numerous  tie  lines  that  it 
is  not  supposed  that  any  measurable  error  could 
accumulate  within  this  section;  its  whole  adjust- 
ment was  therefore  made  to  depend  for  initial 
direction  and  length  on  the  above  fixed  triangle. 
In  this  section  there  are  24  conditions  to  be  sat- 
isfied and  42  directions  to  be  corrected. 

The  approximate  elevations  of  the  stations  are 
as  follows: 


Humpback 

Spear 

Tobacco  Row 

Long  Mountain 

Flat  Top 

Cahas 

Smith  ]Mountain 

Moore 

Buffalo 


Meters. 
I    1 10  "4 

491  7 

S94  ■  S 

436-8 

I    21S7 

I  088  '4 

622  7 

784  -o 

I   210-4 


Feet. 
3  643 

1  613 

2  936 

1  433 

3  998 
3  571 

2  043 

2  572 

3  971 


Corrections  to  horizontal  directions  for  height  of 
station  observed  upon  were  applied.     Squaring  the 

closing  errors  of  the  triangles  we  get-w  — 


28 


i"-52 


as  the  mean  error  of  a  triangle,  also  mean  error  of 

I  '^2 

an  angle  —f-  —  dszo"-9,S  and  the   probable  error  of 
a  direction  =ito"'42. 


THE    MAIN    TRIANGULATIOX. 


149 


/Ihsirads  of  horizontal  dnrcHo)n  al  stations  tonipositijr  the  first  section  of  the  trianfridation  south  of 
the  t  ran  scon  tiuen  tat  triangutation,  /Sy;  to  iSjg. 

I/uinpbac/c,  Nelson  County,  Virginia.  June  8  to  29,  1875.  A.  T.  Mosnian,  observer.  35""  direction 
theodolite  No.  10.  May  j  i  to  June  6,  1S78.  A.  T.  Mosman,  observer.  50'-"*  direction  theodolite 
No.  114.  August  18  to  28,  1879.  A.  T.  Mosnian  and  W.  B.  Fairfield,  obsers-ers.  50""  direction 
theodolite  No.  114. 


No.  of 
direc- 
tions. 


Objects  observed. 


Corrections 


Corrections 
from  ad- 


kesMltsof  local  ^T/"  f.!:'"';';   KesultinK  Reductions  KesultinK  :,;™"' li'/^f 
adjustment.      'Jninsc'mti      *^'^™nds.    tosea  level,    seconds.   ^"^"fiV^"'"^ 


nental  arc. 


Final 
seconds. 


Jarman 

Spear 

I<ong  Mountain 

Tobacco  Row 


0  00  00  "GO 

126  14  25 '02 

154  41  57-10 

173  06  07  •6S 


-O-Sy 


25  '46 


(57"i') 


06 -81 


4-0  -46 


57 -57 


Probable  error  of  a  single  observation  of  a  direction  {D.  and  R. ),  e,  =  ±\"'2'i^.     Circle  used  in  XI 
positions. 

Spear,  Buckingham  County,  Virginia,     July  30  to  August  29,  1875.     A.  T.  Mosnian,  ob.server.     35™ 

direction  theodolite  No.  10. 


Willis 

2 

Long  Mountain 

3 

Smith  Mountain 

4 

Flat  Top 

Tobacco  Row 

Humpback 

0 
113 
ng 
150 
i6o 

ou 

14 
19 

uo 

00 
•50 
•25 
49 

•42 
•50 

+0 

(26 
(24 
(15 

•53) 
29) 
■52) 

-l-o 

24 

-1-0 

•04 
03 

•oS 

-1-0 

■33 

17 

59 

43 
02 

-Ho 

43 
02 

■64 
■06 

233 

-0 

44 

26 -yS 

24  '21 
15    19 


Tobacco  Ro2i\  Amh&rai  County,  Virginia.  vSeptember  14  1023,1875.  A.  T.  Mosnian, 
direction  theodolite  No.  10.  September  6  to  9,  1879.  A.  T.  IMosman,  observer, 
theodolite  No.  114. 


8 

Flat  Top 

0 

00 

00  "oo 

Humpback 

140 

52 

23-38 

4-0-86 

24-24 

Spear 

200 

19 

28-80 

—0-22 

28-58 

Willis 

208 

43 

28 -06 

5 

L,ong  Mountain 

272 

56 

37 '39 

Lynchburg 

276 

15 

52  -23 

6 

Smith  Mountain 

318 

30 

40-14 

7 

Cahas 

345 

52 

24  -62 

4-0-06 


(00-06) 


observ 
4-0-93 


•er.     35^' 
direction 


°°  9) 


(37 '37) 


37 'SO 


4-0-04 

(40-lS) 

4-0  07 

40  -25 

-ho -07 

(24-691 

-0-S7 

23 -82 

^.).^' 

=  ±i"-43. 

Probable  error  of  a  single  observation  of  a  direction  [D.  and  R.),  c, 

Loiiff  i\fountain,  Campbell   County,    Virginia.     October  16   to    December  9,  1S75.     A.    T.   Mosman, 

observer.     35^'"  direction  theodolite  No.  10. 

1.       seconds.      a(,j„st,-,,ent       seconds. 


Number  of 
directions. 


Objects  observed. 


Results  from  local 
adjustment. 


Reduction 
tosea  level 


12 
13 
14 

9 
10 
II 


Tobacco  Row 
Humpback 
Spear 
Willis 

Smith  Mountain 
Cahas 
Flat  Top 

Azimuth  Mark,  Lynchburg 
C.  H. 


o  00  00  'OO 

29  31  39 '55 

60  19  37  -53 

86  30  ,44  "3^ 

25 1  12  44  -36 

273  5'"*  20  -77 

309  05  1 2  -49 

356  02  42  -35 


-0-03 
+0  -03 
+0  -03 

+  0-04 
^o  -04 
— o  -05 


59  "97 
39 '58 
37 '56 


44  '40 
20  -S3 
12-44 


-o  -24 
+0-84 
—0-50 

+0-47 
-0-47 
— o  -lo 


59 

■73 

40 

•42 

37 

•06 

44 

•-'^7 

20 

•36 

12 

■34 

Probable  error  of  a  single  observation  of  a  direction   {/^.  and  A".),  t\- 
XXIII  positions. 


:i"'36.     Circle  useii  in 


I50 


THE    EASTERN    OBLIQUE    ARC. 


.-Ids/rac/s  of  horizontal  directions  at  stations  coiiiposini:^  the  Jirst  section  of  the  trianffulation  south  of 
the  transcontitienla!  triaiigiilatioji,  iSy§  to  iSjg — continued. 

Flat  Top,  Peaks  of  Otter,  Bedford  County,  Virginia.     June  20  to  September  2    1876.     A.  T.  Mosman, 

observer.     35' "'  direction  theodolite  No.  10. 


Vumber  of 
directions. 

Objects  obsen.'e(l 

•5 

Tobacco  Row 

16 

Spear 

Lynchbursj 

17 

Lon.£(  Mountain 

18 

Smith  Mountain 

19 

Moore 

20 

Cahas 

21 

Buffalo 

Results  from  local      Reductions      Resulting   Corrections 

adjustment.  to  sea  level.       seconds.     'TO'"  ng"''f 

■"  adjustment. 


Final 
seconds 


O  00  00  '00 

10  17  00 '26 

26  12  24  '16 

42  01  51  79 

108  18  02  '38 

138  23  14-12 

156  09  54  -25 

157  53  45 '03 


-Ho  -04 
-f  o  'OI 

~0  '02 
O  '00 

+0-05 
-Lo-o8 
-f  o  -oS 


00  '04 
00  '27 


Probable  error  of  a  single  observation  of  a  direction  (/).  and  R. 
XXIII  positions. 


51  77 
02-38 
14-17 
54 '33 
45  Ti 


— o  -28 
—0-13 

— Q-II 

--o-o8 
+0-09 
+  0-40 

-l-O  -12 


5976 
00-14 


51-66 
02-30 
14  -26 
54  73 
45 '23 
d=i"-36.     Circle  u.sed  in 


Cahas,  P'ranklin  County,  Virginia.     June   25  to  July  13,  1877.     A.  T.  Mosman,  observer.     50'^"'  direc- 
tion theodolite  No.  114. 


32 

Smith  Mountain 

33 

Moore 

34 

Buffalo 

29 

Flat  Top 

30 

Tobacco  Row 

31 

L,ong  Mountain 

O  00  00  -QO 

90  56  57  '57 

1 23  26  54  -08 

300  01  07  -25 

309  43  37  '90 

330  46  17  -45 


— o  -02 

40-03 
+o-o8 
+0-09 
+0  -06 
+0  -01 


Probable  error  of  a  single  observation  "f  a  <lirection  {D.  and  R. ' 
positions. 


59  "98 
57 '60 
54-I6 
07 '34 
37-96 
17-46 

<',  =  zbo" 


— o  -06 
— o  -84 

-0-15 
+0-36 
-0-38 

fl-07 

71.     Circle  used  in  XI 


59-92 

56  -76 

54 

•01 

07 

-70 

37 

■58 

18 

■53 

Smith  Ilfountani,    Pittsylvania  Count}-,  Virginia.     August  6  to  September  6,    1877.     A.   T.    Mosman, 
observer.     50""    direction  theodolite  No.  114. 


24 


Cahas 


25 

Flat  Top 

26 

Tobacco  Row 

27 

Spear 

28 

Long  Mountain 

22 

Moore 

Bull  Mountain 

23 

Buffalo 

o     00     00  -00 


-o  -04 


59-96      -0-19 


59 '77 


72 

09 

19  84 

O'OO 

19  -84 

+o-i8 

20  -02 

102 

22 

00  -94 

+0-05 

00  -99 

-|-o  -06 

01  -05 

123 

12 

35-99 

+0-03 

36 -02 

-0-18 

35-84 

128 

00 

47-72 

+0-03 

47-75 

-0-48 

47-27 

297 

18 

17-97 

+0-05 

18-02 

+0-47 

18-49 

312 

53 

58  '97 

.... 

327 

37 

19 -51 

+0-05 

19-56 

+  0-13 

19-69 

)n  of 

a  direction 

[D.  and  A^l 

,  ^i  =  ± 

o"-68.     Circle  used  in 

XI  positions. 


THK    MAIN    TRIANGULATION. 


151 


► 


I 


Abstracts  of  hofizontal  directions  at  stations  co)iiposin,i,r  the  first  section  of  the  trianf^iilatioii  soulli  of 
the  transcontinental  Iriani^Hlat'iOH,  /Hy^  to  z,?/!;; —continue'!. 

Moore,  Stokes  County,  North  Carolina.     November  7  to  December  26,  1876.     A.  T.  Mo.sman,  observer. 
35""  direction  theodolite  No.  10.     April  21  to  May  31,  1877.     Same  observer  and  instrument. 


Number  of 
directions. 

objects  oljserved 

Pilot  Mountain 

39 

Buffalo 

Azimuth  Mark 

40 

Cabas 

41 

Flat  Top 

42 

Smith  Mountain 

Young 

Poore 

Kesults  from  local       Reductions       Resulting     f  "I'.^ffi'jl'",'' 
adjustment.  to  sea  level.        seconds,      adjustmeiit. 


Hinal 
seconds. 


0 

fX3 

00  -oo 

89 

04 

10 '07 

— G05 

10  02 

-023 

0979 

no 

3' 

01  -90 

127 

05 

24  -85 

+0-04 

24  -89 

+  1  -48 

■    26  37 

138 

23 

02  '84 

+0-07 

02  91 

-0  -58 

02-33 

153 

26 

SI  -69 

+0-04 

57  73 

-0-68 

57-05 

314 

44 

12-49 



354 

21 

09  '66 

Probable  error  of  a  single  observation  of  a  direction  [D.  and  R. ),  t',= 
XXIII  positions  in  1S76  and  in  XXIV  positions  in  1S77. 


ri^'SS.     Circle  used  in 


Btill  Mountain 

38 

Moore 

Pilot  Mountain 

Young 

Poore 

35 

Flat  Top 

36 

Cahas 

37 

Smith  Mountain 

— 0  -04 

48 -88 

+0-10 

48-98 

-fo-09 

00  -82 

--0-44 

00-38 

+o-o8 

56  -67 

—0  04 

56-63 

+0-02 

26-87 

rO-3S 

27-25 

Buffalo,    Floyd    County.    Virginia.     September    25    to  October     16,    1S76.     A.  T.  Mosman,  observer. 

35^"'  direction  theodolite  No.  10. 

o  /  //  //  //  //  // 

O       00       00  -QO 

41    36   48 -92 
62    51    49-89 

70  37  50  -34 

99  35  20  -42 

290  26  00  -73 

292  07  56  -59 

316  18  26 -85 

Probable  error  of  a  single  observation  of  a  direction  [D.  and  A'.),  Ct  =  ±i"'5S.     Circle  used  in 
XXIII  positions. 

Observation  equations. 

0=  +  I-I2  +  (l)-(2)-(l3)  +  (l4) 

o=-o-54-(i)  +  (5)-(i2)  +  (i3) 
o=~i-4o-(4)  +  (S)-  (i5)  +  (i6) 

o=-i-03-(5)  +  (8)-(ii)  +  (i2)-(i5)  +  (i7) 
o=+o-09-(3)  +  (6)-(26)+(27) 
o=  +  i-6o-(2)+(3)-(9)  +  (i4)-(27)  +  (28) 
o=-o-95  '  (6)  +  (8)-(i5)  +  (i8)-(25)  +  (26) 
o=-r74^(7)  +  (S)-(i5)  +  (2o)-(29)+(3o) 
o=-o-S8-(5)  +  (7)-(io)  +  (i2)-(3o)+(3i) 
o=+o-37-(6)  +  (7)-(24)  +  (26)-(3o)  +  (32) 
0=  -i-o7-(i8)  +  (2i)-(23)  +  (25)-(35)  +  (37) 
o=-o'63-(2o)  +  (2i)  +  (29)-(34)-(35)  +  (36) 

0=+0-23-(lS)  +  (l9)-(22)+(25)-(4l)  +  (42) 


I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 


152  THE    EASTERN    OBLIQUE    ARC. 

Observation  equations    continued. 

XIV     o=+3-6o-{22)  +  (24)-(32)+(33)-(4o)  +  (42) 
XV     o=  +  ro7-(22)  +  (23)-(37)4  (38) -(39) +(42) 
XVI     o=-674-6-33(i)-r96(2)-2-5i(i2)+37i(i3)-i-2o(i4) 
X\'II     o=+o'30— o'i96( 2) +  1-189(4 )—o' 171  ( ii)+o'29i(  12)  — o-i2o(  14)— o'927(i5)  +  i-i6o(  16) 

-0-233(17) 
XVIII     o=-2-o-r96(5)+2-o6(6)-o-io(S)"2-33(i5)+3-26(i7)-o-93(iS)^r43(25)-t-4-38(26) 
-2-95(28) 
XIX     o=+o-ii~-i-78o(2)  +  r976(3)+o-272(5)-o-2o6(6)— 0-438(26) +  2-505  (27)— 2-067(28) 
XX     o=  +  2-5i— 0-010(5 ) +0-836(7)— 0-826(8)— 0-299(10) +0-470(1 1 )— 0-171(12) — 0-877(29) 

+  i-23i(3o)-o-354(3r) 
XXI  i  0=  + 1-1-3-70(9) +5-02 (10) -I -32(1 1 )-o-93(  17) ^2-83(18) -I -90(20) -I -22(29)  +  3-77(3i) 

-2-55(32) 
XXII     o=+i-46— o-i9o(  i8)+o-656(i9)— 0-466(20)— o- 109(22 )+o-i77(24)—o-o6S( 25)— 0-629(40) 
+  1-054(41) -0-425(42) 

XXIII  0= -4-60-0-190(18) +7-158(20) -6-968(21) -0-332(23) +0-400(24) -0-068(25) -7-099(35) 

+7-56S(36)-o-469(37) 

XXIV  o=-i6-2-i-o9(22)+3-32(23)-2-23(24)-5-43(36)+4-69(37)+o-74(38)-2-69(39) 

+6-94(4o)-4-25(42) 
N.  B.— The  correlate  equations  being  of  a  simple  character,  are  not  given  here. 

Normal  equations. 

C,  C2  C,  C4  C5  C6  C7  Cs  C9         Cio        Cii        Ci2        C13        C14  C15 


0= 

+  1 

■12 

0  = 

—  0 

•54 

0  = 

—  I 

-40 

0= 

—  I 

•03 

0  = 

+0 

■09 

0  = 

+  1 

■60 

0  = 

—  0 

■95 

0  = 

—  I 

■74 

0  = 

-0 

-8S 

0  = 

+0 

■37 

0  = 

-I 

-07 

0  = 

~0 

■63 

0  = 

+0 

-23 

0  = 

+,^ 

-60 

0  = 

+  1 

•07 

+4 


+4 


-t-4 


+  2 
+6 


+4 


+6 


+2 

+  2 

+  2 

+  2 

+  2 

—  2 

—  2 

+6 

+  2 

+  2 

+6 

—  2 

—  2 

+6 

+  2 
+6 

+6 


+  2 
+6 


+  2 


+6 


+2 

+  2 

+6 

+  2 

+6 

THE    MAIN    TRIANGULATION. 
Normal  equations  — coiiipleted. 


153 


No. 

C,6 

Cr7 

Cia 

c„ 

C2, 

C 

C22 

CsT 

C« 

I 

+  3-38 

+o'o76 

+  I -780 

2 

—    O'll 

-0'29I 

-  1-96 

+  0-272 

+0I6I 

3 

+0  -898 

+    2-23 

—0-826 

4 

-  2-51 

+  1-156 

+  7-45 

—    0'272 

- 1 -457 

+  0-39 

5 
6 

-  232 

-  2-95 

+    0-761 

-   o-8i6 

+  076 

+0  -076 

+  3-70 

7 

+0-927 

+  5-05 

-  0-232 

—0-826 

+  2-83 

—0122 

- 

0-122 

8 

+0927 

+  2-23 

+0-446 

-  0-68 

-0-466 

+ 

7-15H 

9 

—  2-51 

+0-291 

+  I  -96 

—    0'272 

— 0611 

-   1-25 

10 

+  2-32 

—  0-232 

-0  -395 

-  2-55 

-0-177 

- 

0400 

+ 

2-23 

II 

-  0-50 

-  2-83 

+0-122 

+ 

o-ii6 

+ 

1-37 

12 

-0-877 

+  0-68 

+0-466 

+ 

0-541 

- 

5  43 

13 

-  0-50 

-  2-83 

-0  -592 

+ 

0122 

- 

3-'6 

14 

+  2-55 

+0-490 

+ 

0-400 

- 

12-33 

15 

—0-316 

+ 

0-137 

- 

I  -10 

16 

0= 

- 

6 

7 

+65-41 

—0-202 

+  3-489 

+0-429 

17 

0= 

+ 

0 

■30 

+3  -S40 

+  I  -400 

+  0-349 

-0-130 

+  0-442 

18 

0= 

- 

2 

0 

+54-95 

+  3-222 

+  0-102 

-  5-664 

+0-274 

+ 

0-274 

19 

0= 

+ 

0 

•II 

+17-929 

-0  -003 

+ 
+ 

■51 
■I 

+  4-131 

-  2-3S6 
+75  -32 

21 

0  = 

I 

+0  -348 

- 

14-138 

22 

0= 

+ 

I 

•46 

+  2-418 

- 

3  224 

- 

2  84 

23 

0= 

- 

4 

•60 

+207-99' 

- 

45  29 

24 

0= 

- 

6 

■2 

+ 

42-67 

A'esull! 

>/g  (orrei 

'ales. 

c.= 

+  0 

•190 

c,= 

=  +  0 

■767 

c..= 

=  — 0 

•196 

c.= 

+0 

•547 

C,o  = 

=  — 0 

•844 

C.8  = 

=+0 

•0145 

C3  = 

+  0 

•093 

c„= 

=  +0 

•134 

c.,= 

=  — 0 

•0569 

C4  = 

-0 

■183 

c„= 

=  +0 

•146 

C.o= 

=— 0 

•603 

C5  = 

— 0 

•5S7 

C,3  = 

=  +0 

■276 

c=.= 

=+0 

•0231 

C6  = 

—  0 

■554 

C.4  = 

:— 0 

•842 

c..= 

=  — 0 

•285 

C;  = 

+  0 

•231 

Cx5  = 

=  +0 

•051 

c„= 

=+0 

•0233 

C8  = 

4-0 

•28S 

C,6  = 

=  +  0 

-129 

C.4  = 

=  +  0 

•0665 

Resulting  eo)  rectious  to  obs 

crved  direetioii 

S". 

(0  = 

=  +0  -460 

(12)  = 

=  — 0"24I 

(23)  = 

=  -^  0 

•130 

134)  = 

=  —0-146 

(2) 

+0-251 

(13) 

+0  -836 

(24) 

— 0 

•187 

(35) 

-0-445 

(3) 

-0  -079 

(14) 

-0  -495 

(25) 

-t-o 

•176 

(36) 

—0  039 

(4) 

-0  -326 

(15^ 

— 0-281 

(26) 

-^0 

•062 

(37) 

-0  -384 

(5) 

-0  -075 

(16) 

-0-134 

(27) 

— 0 

■176 

(38) 

-fO'lOO 

(6) 

+0  -068 

(17) 

—0  -112 

(28) 

— 0 

•479 

(39) 

—0  -230 

(7) 

-0  -869 

(18) 

-0  -077 

(29) 

+0 

•359 

(40^ 

- 1  -483 

(S) 

+  0-926 

(19) 

^0  -089 

(30) 

— 0 

■377 

(41) 

-0  -576 

(9) 

+  0  -468 

(20) 

+0  -398 

(31) 

+  1 

•06S 

(42) 

-0  -677 

(10) 

-0  -471 

(21) 

+0  -118 

(32) 

— 0 

061 

(") 

-0-097 

(22) 

+0  -474 

(33) 

— 0 

•842 

Probable  error  of  an  observed  direction 


o  674  ^/  ^- 


—  =3tO     -41. 


154 


THE   EASTERN   OBLIQUE   ARC. 


I\CS!ill!)ig  aiiglis  and  sidts  of 


Long  Mountain 

Humpback 

Spear 

Tobacco  Row 
Humpback 
Long  Mountain 

Long  Mountain 
Tobacco  Row 

Spear 

Flat  Top 
Tobacco  Row 
Spear 

Flat  Top 

Spear 

Long  Mountain 

Flat  Top 
Tobacco  Row 
Long  Mountain 

Smith  Mountain 
Tobacco  Row 
Spear 

Smith  Mountain 

Spear 

Long  Mountain 

Smith  Mountain 
Flat  Top 
Tobacco  Row 

vSmith  Mountain 
Tobacco  Row 
Long  Mountain 

Smith  Mountain 
Flat  Top 
Spear 

Smith  Mountain 
Flat  Top 
Long  Mountain 


the  first  section  of  the  triaugulatioii 
net  and  extension. 


sont/icuest  of  the  Kent  Island  ttase 


Observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances. 

Distances  in 
meters. 

o 

/ 

// 

// 

1/ 

// 

30 

47 

57-98 

-I  -33 

56-65 

I  -35 

4-649 

2S3  4 

44  594  -71 

2.S 

27 

31  "65 

+0-46 

32-11 

I  '35 

4-618 

077  4 

41 

502  -80 

120 

44 

35  '53 

-0-25 

35-28 

1-34 

4-874 

224  9 

74 

855  -71 

132 

04 

13 '13 

-0  -qS 

13-05 

1  -00 

4  -874 

224  9 

74 

■855-71 

iS 

24 

0970 

—0  -46 

09  -24 

0-99 

4-502 

886  6 

31 

833  -66 

29 

31 

39  '61 

+ 1  -08 

40-69 

0-99 

4-696 

339  6 

49 

698  -08 

60 

19 

37-59 

-0  -25 

37-34 

0-97 

4  -577 

326  2 

37 

785  -59 

72 

37 

0879 

—0  -07 

08  -72 

0-98 

4-618 

077  4 

41 

502  -So 

47 

03 

17-11 

-0-25 

16 -86 

0-97 

4-502 

886  7 

31 

833  -67 

10 

J7 

00-23 

+0-15 

00-38 

0  -41 

4-577 

326  2 

37 

785  -59 

159 

40 

31  -48 

fo-92 

32-40 

0  -41 

4-866 

398  9 

73 

518-88 

10 

02 

28  -12 

+0-33 

28  -45 

0  -41 

4  -567  083  6 

36 

904  -86 

31 

44 

51  -50 

+0  -02 

51  -52 

1-56 

4  -618 

077  4 

41 

502  -80 

37 

oo 

48-99 

-0-57 

48-42 

1-56 

4-676 

543  I 

47 

483  -54 

III 

T4 

25  -12 

-0-39 

24-73 

I  -55 

4  -866 

398  9 

73 

518  -88 

42 

01 

51   -73 

+0-17 

51  -90 

0-99 

4-502 

886  7 

31 

833  -67 

ft7 

03 

22  -69 

+  1  -00 

23-69 

I  -00 

4-676 

543  2 

47  483  -55 

50 

54 

47-53 

—0  -14 

47-39 

0-99 

4  -567  083  6 

36 

904  -86 

20 

50 

35  -03 

—0  -24 

34-79 

I  96 

4-577 

326  2 

37 

785  -59 

118 

II 

II  -60 

+0-07 

II  -67 

I  -97 

4-971 

303  I 

93 

605-87 

40 

5« 

^9-35 

+0  -08 

19-43 

I  -96 

4-842 

815  4 

69  633  -05 

4 

48 

"  -73 

—0-30 

11-43 

0-35 

4-61S 

077  4 

41 

502  -80 

6 

04 

57-76 

-0-33 

57  -43 

0-35 

4  -720  334  2 

52 

521  -14 

69 

06 

53-16 

-0-97 

52-19 

0-35 

4-971 

303  0 

93 

605  -85 

30 

12 

41  -15 

—0  -11 

41  -04 

I  -44 

4-567 

083  6 

36 

904  -86 

108 

18 

02  -34 

+0  -20 

02-54 

I  -44 

4-842 

815  2 

69  633  -02 

41 

29 

19-88 

+0  -86 

20-74 

I  -44 

4-686 

522  8 

48  587  -30 

25 

3« 

46-76 

-0-55 

46  -21 

1-34 

4-502 

886  7 

31 

833  -67 

45 

34 

02-81 

+0-14 

02-95 

1-34 

4-720 

334  4 

52 

521  -17 

loS 

47 

15-57 

--0-71 

14  -86 

'  -34 

4  -842 

815  4 

69 

633  -05 

51 

03 

16-18 

-0-35 

>5  -83 

3-00 

4  -S66 

398  9 

73 

51S-88 

98 

01 

02-11 

+o-o6 

02  -17 

2-99 

4-971 

303  I 

93 

605  -87 

30 

55 

5f  -23 

—0  -24 

50-99 

3-00 

4  -686 

522  9 

48 

587  -31 

55 

5> 

27  -91 

-0  -66 

27-25 

1-79 

4-676 

543  2 

47 

4S3  -55 

66 

16 

10  -61 

+0-03 

10  -64 

I  -79 

4-720 

334  3 

52 

521   16 

57 

52 

2S  -04 

-0-56 

27-48 

I  -79 

4-686 

523  0 

48  587  -33 

No. 


'3 


14 


15 


16 


17 


IS 


19 


23 


24 


THE 

M 

AIN    TI 

ilANGU 

LATIC 

>N. 

^5S 

Itiyii^  angles  and  sides 

(if  the  first  scclion  of  the  Iriangu 

lation 

southwc 

v/  if  the  Kent  Island  fiase 

Ul 

■/  a)i 

d  extension — continued. 

Stations. 

(Jhservcc 

aiiKles. 

Correc- 
ti<jii. 

Spher- 
ical 
aiif;les. 

Spher- 
ical 
excess. 

I-()K.  dis- 
tances. 

Distances  in 
meters. 

i 

0 

f 

// 

// 

// 

// 

Calias 

9 

42 

30-62 

-0-73 

29-89 

0  -67 

4  -567 

083 

6 

36 

904  -86 

Flat  Top 

156 

09 

54-29 

+0  -68 

54-97 

0-68 

4  946  643 

2 

88 

438  -88 

Tobacco  Row 

14 

07 

35  '37 

+ 1  -79 

37-16 

0  -67 

4-727 

663 

4 

53 

415-02 

Cahas 

21 

02 

39  '50 

+ 1  -44 

40  -94 

2  -28 

4  -502 

886 

7 

3' 

•833  -67 

Tobacco  Row 

72 

55 

47  -32 

-0  -79 

46-53 

2-28 

4  -928 

119 

5 

84  746  06 

Long  Mountain 

86 

01 

39 '>4 

I  0-23 

39  "37 

2-28 

4  -946  643 

2 

88 

438  -88 

Cahas 

30 

45 

1012 

fo-71 

10  -83 

I    96 

4-676 

543 

2 

47  483  -55 

Flat  Top 

114 

08 

02  -56 

H  "-51 

03  -07 

I   -96 

4  -928 

119 

6 

84  746-08 

Long  Mountain 

35 

06 

51-61 

+0-37 

51  -98 

1-96 

4-727 

663 

6 

53 

415  05 

Cahas 

59 

5S 

52-64 

--(J  -42 

52-22 

1-63 

4  -686 

522 

9 

48  587-31 

Flat  Top 

47 

51 

51  '95 

i-o  -48 

52-43 

■  -63 

4-619 

220 

5 

41 

612-18 

Smith  Mountain 

72 

09 

19-88 

-f  0  -36 

20  -24 

■■63 

4-727 

663 

5 

53 

415-04 

Cahas 

29 

'3 

42-52 

-I  -'3 

41  -39 

1  -46 

4-720 

334 

3 

52 

521  -16 

Long  Mountain 

22 

45 

36-43 

—0-94 

35-49 

i   -46 

4-619 

220 

5 

41 

612-18 

Smith  Mountain 

128 

00 

47 '79 

—0-30 

47-49 

1  -45 

4-928 

119 

6 

84  746-08 

Cahas 

50 

16 

22  -02 

+032 

22  -34 

2  40 

4  -842 

815 

4 

69 

633  05 

Tobacco  Row 

27 

21 

44-51 

-0-94 

43  -57 

2  -40 

4-619 

220 

6 

41 

612  -19 

Smith  Mountain 

102 

22 

01  -03 

+0-25 

01  -28 

2-39 

4-946  643 

3 

88 

438  -90 

Buffalo 

25 

52 

26-05 

+0  -83 

26-88 

3-38 

4  -686 

522 

9 

48 

587  -31 

Flat  Top 

49 

35 

42-73 

+0-19 

42-92 

3  -38 

4  -928 

312 

3 

84 

783-69 

Smith  Mountain 

104 

32 

GO  -28 

+0-05 

00-33 

3  -37 

5  -032 

535 

0 

107 

779-2 

Buffalo 

I 

41 

55-85 

H0-41 

56-26 

0-15 

4-727 

663 

5 

53 

415-04 

Flat  Top 

I 

43 

50-78 

-0-2S 

50-50 

0-15 

4  '735 

698 

3 

54 

412-45 

Calias 

176 

34 

13     18 

+0  -50 

13 -68 

0-14 

5  -032 

534 

9 

107 

779-2 

Buffalo 

24 

10 

30  -20 

■  0-42 

30  62 

1  -60 

4-619 

220 

5 

41 

612-18 

Flat  Top 

123 

26 

54-18 

0  -08 

54-10 

I  60 

4  928 

312 

3 

84 

7S3  -69 

Smith  Mountain 

32 

22 

40-40 

-0-32 

40  -oS 

I  60 

4  -735 

698 

6 

54 

412-49 

Moore 

15 

03 

54-82 

—0  -10 

54-72 

2-73 

4  -686 

522 

9 

48 

587  -31 

Flat  Top 

30 

05 

II   -79 

-10-17 

1 1  -96 

2  73 

4-971 

803 

6 

93 

713 -Si 

Smith  Mountain 

T34 

5" 

01   -82 

—0  -30 

(11  -52 

2-74 

5-Ii2 

329 

4 

I  ^2 

534  -6 

Moore 

II 

17 

38  -02 

-2  06 

35  96 

1  -'X^ 

4  727 

663 

5 

53 

415-04 

Cahas 

15  J 

55 

50  -26 

—  1  -20 

49  -06 

1-83 

5-122 

329 

5 

132 

534  -6 

Flat  Top 

17 

46 

40  - 1 6 

4  "-3' 

40-47 

1  -83 

4  -920 

554 

4 

83 

2S2  -62 

Moore 

26 

21 

32  -84 

-2-i6 

30  -68 

2-93 

4-619 

220 

5 

41 

612   iS 

Cahas 

90 

56 

57  -62 

— 0-7S 

56  -84 

2-94 

4-971 

803 

6 

93 

713-81 

Smith  Mountain 

62 

41 

41  -94 

-0-66 

41-28 

2-93 

4  920  554 

3 

83 

282  60 

156 


THE   EASTERN   OBLIQUE    ARC. 


No. 


25 


26 


27 


Itinff  angles  and  sides  of  the  fir. 

/  sec 

lion  of  the  triangulation 

southwest  of  th 

■  Kent 

Island  base 

n 

't  at 

d  extension  — continued. 

stations. 

Obser\-ed 

insjles. 

Correc- 
tion. 

Spher- 
ical 
anarles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances. 

Distances  in 

meters. 

0 

/ 

// 

// 

" 

// 

Moore 

49 

iS 

52  -89 

-0-35 

52  -54 

4-04 

5  -032 

535 

0 

107   779-2 

Buffalo 

in 

10 

48-06 

-F  0  -55 

48-61 

4-04 

5-122 

329 

3 

132  534  -6 

Flat  Top 

19 

30 

30-94 

+0-03 

30  -97 

4-04 

4-676 

356 

4 

47  463-13 

Moore 

3S 

01 

14  -87 

+  1-71 

16-58 

2  -06 

4-735 

698 

6 

54  412  -49 

Buffalo 

109 

2.S 

52-21 

+0-14 

52  -35 

2  -06 

4  -920 

554 

3 

83  2S2-60 

Cahas 

32 

29 

56  -56 

f  0  -69 

57-25 

2  -06 

4-676 

356 

4 

47  463-13 

Moore 

64 

22 

47  7  [ 

-0-45 

47-26 

3-40 

4-928 

312 

3 

84  783  -69 

Buffalo 

W5 

18 

22  -oi 

-0-28 

21  -73 

3-39 

4-971 

803 

6 

93  713-81 

Smith  Mountain 

30 

19 

or  -54 

-0-34 

01  -20 

3-40 

4-676 

356 

4 

47  463-13 

No.  24. 


5.  SECOND  OR  NORTH  CAROLINA  SECTION  OF  THE  TRIANGULATION  SOUTH  OF  THE 
TRANSCONTINENTAL  TRIANGULATION,  IN  VIRGINIA  AND  NORTH  CAROLINA,  1876- 
1895. 

This  section  extends  over  an 
area  covered  by  several  large  tri- 
angles which  have  the  centrall}' 
located  station  Poore  as  one  of 
their  points  in  common.  In  1878 
when  the  main  triangulation  be- 
tween the  lines  Buffalo  to  Moore 
and  Grassy  to  Sawnee  was  ad- 
justed, this  central  figure  about 
Poore  had  no  existence.  In  con- 
sequence of  the  introduction  of 
this  figure  some  modification  in 
the  treatment  of  the  work  be- 
tween the  Kent  Island  and  At- 
lanta bases  became  necessary. 
The  adjustment  of  1878  involved 
considerable  labor,  as  it  included 
the  formation  and  solution  of  41 
normal  equations.  It  was  de- 
sirable to  retain  this  adjustment 
and  interpo.se  the  central  figure 
about  Poore  for  the  purpose  of 
disposing  of  whatever  error  was 
developed  between  the  bases  by 
the  intervening  triangulation. 
The  probable  error  of  the  meas- 
ure of  the  Kent  Island  base, 
which  is  the  least  accurate  of  the  six  bases  along  the  arc,  is  34  units  in  the  seventh 
place  of  decimals  of  its  logarithm,  whereas  that  of  the  Atlanta  base  is  but   10  units; 


Bixffbdo 

/ 

V 

. — /A 

Rogers^__ 

/     /\ 

'    /\ 

iMoore\ 

/                            \                / 

jf^ 

yRoan  High  Bhi/T                          \  /^^^ 

\ 

\                                                        -^KFaure 

\  /7_ 

-"^yYouTig 

Benri.  \                          /                       / 

y^ing 

KUometers 

10         0          iO        20        30        40         50        60        70        80         90       100 

UO       120      UO      IV)      150 

Statxite  Miles 

10                0                10               20              M              40               50              60 

70              80               90 

THE   MAIN   TRI ANGULATION. 


0/ 


hence  the  influence  of  the  latter  over  tlie  trianj^ulation  between  stations  Sawnee  and 
Benn,  which  constitutes  the  third  section,  was  retained.  In  the  present  central  fij^ure 
the  condition  was  introduced  preserving  the  fixed  relation  between  the  two  sides  marked 
in  the  diagram  by  heavy  lines. 

The  approximate  elevations  of  the  stations  are  as  follows: 


Poore 

Young 

Benn 


eters. 

Keet, 

817 

2   680 

King 

333 

I   093 

Roger.s 

886 

2   907 

Roan  Higli  Bluff 

Meters.  Feet. 

516  I   693 

I    746  5   729 

I  913  6 


'/O 


From  the  eleven  triangles  we  derive  the  mean  closing  error  of  a  triangle 


/56-8_ 
'     II 


2  '27 
2""27,  the  mean  error  of  an  angle — 7= 

^3 


zb  I  "'5 1  and  the  probable  error  of  a  direc- 


tion   o'674 


2'27 


±  o"'63. 


In  the  preceding  diagram,  the  two  heavy  lines  are  fixed  in  length,  and  the  disper- 
sion of  the  di.screpancy  between  the  bases,  of  24  units  in  the  .seventh  place  of  decimals 
in  the  logarithm,  is  accomplished  by  the  adjustment.  Attention  is  called  to  the  fact 
that  in  a  figure  adjustment,  when  forcing  an  accord  l)etween  the  fixed  lengths  of  two  ter- 
minal sides,  as  is  the  ca.se  here,  the  conditional  eqriation  may  be  established  either  with 
plane  angles  or  with  spherical  angles,  provided  in  the  latter  case  the  terminal  sides  are 
corrected  for  difference  between  arc  and  sine.  This  is  readih-  done  by  means  of  the  table 
given  in  Coast  and  Geodetic  vSurvey  Report  for  1894,  Appendix  Xo.  9,  page  289,  below 
the  heading  "Table  of  corrections  to  longitude  for  difference  in  arc  and  .sine." 

In  e.stabli.shing  the  length  equation  for  any  unadjusted  figure  the  apparent  dis- 
crepancy to  be  dispersed  in  order  to  produce  accord  between  two  lines  who.se  length  is 
fixed  will  vary  with  the  angles  selected.  The  true  discrepancy  to  be  dispersed  can, 
lievertheless,  be  obtained  from  the  length  equation,  provided  the  length  equation  l^e 
taken  last  in  the  .solution  of  the  normal  equations,  thus  eliminating  all  the  other  unknown 
quantities;  and  the  di.screpancy  so  derived  is  the  same  as  would  beobtained  if  the  length 
equation  were  formed  after  the  entire  figure  had  been  adjusted  in  all  other  respects. 

In  the  present  .section  the  length  di.screpancy  with  the  uncorrected  .spherical  angles 
was  78  units;  but  the  true  di.screpancy  out.stauding  after  the  other  adjustments  are  made 
is  but  24  units.  This  is  less  than  the  probable  error  of  the  mea.surement  of  the  Kent 
Island  base.  The  logarithm  of  the  length  of  line  Buffalo  to  Moore  is4"676  356  4,  and 
that  of  the  line  Benn  to  King,  4'705  136  6. 


158 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  hoyizontat  directions  at  stations  composing  the  second  or  North  Carotina  section  of  the 

triangiilation ,  /Syd-iSg^ . 

Buffalo,  Floyd  County,  Virginia.  September  25  to  October  16,  1S76.  35  ^™  direction  theodolite  No.  10. 
A.  T.  Mosman,  oVjserver.  September  27  to  October  i,  1S95.  45^™  direction  theodolite  No.  4. 
A.  H.  Buchanan,  observer. 


^^1       Objects  Observed. 


Corrections  Corrections 

D        1*  „r  1   „„i  R.euuc-      D„^, ,,,;„„      from  ad-       Result-      from  ad-        „•.  „, 


Reduc- 
tions to 
sea  level. 


first  sec- 
tion. 


onds.      second  sec- 
tion. 


(48-98) 


O      GO      00  •QO  .... 

41       36      48-92  —0-04 
62       51       49  -89 

70    37     50-34  +0-01 

99     35     20-42  +0-05 

144     29     13  -76  +0  -04 

290     26    00-73  +0  '09 

292     07     56-59  -fo-o8 

316     18     26-85  +0-02 

Probable   error   of   a    single    observation  of   a    direction    { /).  and   A".),    (Buchanan,    observer), 
c,  =  ±  i"-25.     Circle  used  in  XI  positions. 


Bull  Mountain 

Moore 

Pilot  Mountain 

3 

Young 

4 

Poore  t 

5 

Rogers  *t 

Flat  Top 

Cahas 

Smith  Mountain 

48  -88 

50-35 
20-47 
13-80 
00  -82 
56  -67 
26  -87 


— o  -63 
—0-19 

+0-74 


-0-44 
— o  -04 

+0-38 


(00-38) 

(56-63) 

(27 '25) 


49  72  ■ 
20  -28 

14 '54 


Moore,  Stokes  County,  North  Carolina.     November  7  to  December  26,  1876,  and  April  21  to  May  31, 
1877.     35^"'  direction  theodolite  No.  10.     A.  T.  Mosman,  observer. 


Pilot  Mountain 

0 

on 

on 

-on 

Buffalo 

89 

04 

10 

-07 

— 0 

■05 

10 

•02 

— 0 

•23 

(09 

-79) 

Azimuth  Mark 

1 10 

31 

05 

01 

•90 

•85 

Cahas 

127 

24 

+0 

-04 

24-89 

+  1 

-48 

(26-37) 

Flat  Top 

138 

23 

02 

•84 

+0 

•07 

02 

-91 

— 0 

-58 

(02 

-33) 

Smith  Mountain 

153 

26 

57 

•69 

+0 

-04 

57 

-73 

— 0 

-68 

(57 

-05) 

i 

Youtig 
Poore 

314 
,354 

44 
21 

12 

■49 
-66 

-fo 

-02 

12 

-51 
-71 

—0 

2 

09 

+0 

■05 

09 

+0 

01  -go 


T2-,^3 
09-83 


♦Reduction  to  center  — 2"'io,  applied. 


fBuchaiiati,  observer. 


THE    MAIN   TRIANGULATIOX. 


159 


Abstracts  of  horizontal  directions  at  stations  comfiositig  the  second  or  North  Carolina  section  of  the 

trian}; Illation,  i8j6-i8qs — continued. 

Poore,  Wilkes  County,  North  Carolina  September  15  to  October  11,  1877.  50""  direction  theodo- 
lite No.  3.  C.  O.  Routelle,  observer.  Auj^ust  30  to  September  17,  1895.  45 '•'"  direction  theoflolite 
No.  4.     A.  H.  Buchanan,  observer.     Circle  used  in  XI  positions  in  both  years. 

Corrections 


Number  of 
directions. 

ObjeclJ 

.  observed. 

Result  of  local 
adjustment. 

Approxi- 
mate 
probable 
errors. 

Reduc- 
tions to 
sea  level. 

Resulting 
seconds. 

from  ad- 
justment 
of  .second 

section. 

Final 
seconds. 

0 

/ 

// 

/> 

., 

// 

// 

// 

Mark 

1877 

0 

00 

00  -00 

±0-07 

6 

Buffalo 

i«77.  1895 

32 

47 

15-52 

0  -12 

+0  -08 

15-60 

-0-39 

15-21 

7 

Moore 
Mark 

1877 
1895 

60 

60 

05 
55 

54  ■■13 

18-32 

0  -II 

+0-04 

54-47 

4-0-02 

54-49 

8 

Young 

1877 

123 

21 

iS  -64 

0  -16 

0  -02 

18  -62 

4-0 -18 

iS-So 

Anderson 

1877 

170 

22 

26-64 

0-28 

9 

King 

1877 

'85 

26 

51  -63 

0-13 

-j-O  -QI 

51  -64 

-0-15 

5'  -49 

10 

Benn 

1877,  1895 

217 

22 

12   19 

012 

+  0  -06 

12-25 

-0-18 

12-07 

Mount  Mitchell     1877 

249 

45 

OS -56 

0-54 

II 

Roan  High 

Bluff    1895 

270 

23 

04-91 

—  0  -02 

04-89 

+0-36 

05  -25 

12 

Rogers 

1895 

329 

46 

41  -23 

— o-io 

41  -13 

^0  -16 

41  -29 

Probat 

)le  error  of  a 

single  observation  of  a 

direction  [D.  and  R.  )  in 

1877,  c,  = 

--±:o"-jS: 

in  1S95, 

VoHnj^,  Rowan    County,   North  Carolina.     September  22    to    November    11,    1S76.     50""    direction 
theodolite  No.  3.     C.  O.  Boutelle,  observer.     Circle  used  in  XI  positions. 


±0  -oS         

0-19  +0-02      09-38 

0-17         

0-14  +0-04       18 -23 

o-r6  +0-04      38 -32 

O  -12  

0-16  +0-02         5497 

o-is  o -06       29-26 

Probable  error  of  a  single  observation  of  a  direction  [^D.  and  A'. ),  t'l  =  j=o"- 


Azimuth  Mark 

0 

00 

00  -oo 

16 

Buffalo 

0 

01 

09-36 

Mocksville  Church 

16 

37 

17-07 

17 

Moore 

16 

40 

18  -19 

13 

King 

218 

37 

38 -28 

Anderson 

237 

26 

03-64 

14 

Benn 

251 

II 

54 '95 

15 

Poore 

299 

32 

29  -32 

00   00 

+0-64 

10  -02 

-0-52 

IS  75 

-I  -40 

36-92 

-1-0 -37 

55-34 

—  0'12 

29-14 

i6o 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directions  at  stations  composing  the  second  or  North  Carolina  section  of  the 

triangidation,  iSyd-iSg^ — continued. 

Benn,  Burke  and  Cleveland  Counties,  North  Carolina.     July  25   to  August  22,1877.     50""  direction 
theodolite  No.  3.     C.  O.  Boutelle,  ob.server.     Circle  used  in  XI  positions. 


Number  of 
directions. 


Objects  observed. 


Results  of  sta-        '^^I'at?'"     ZtsXo    ^^^'^'''^'^  fron't^lnl         F"-J 
tio„  adjustment,     probable   4°'>eVe,.    ^-'=°"d-'*-    adiustSt.      ^^™-'-^- 


Reference  Mark 
Poore 
Young 
Anderson 
King 
Thicketty 
Wofford 
Paris 
Hogback 
Mount  Mitchell 
(  Probable  error  of  a  single  observation  of  a  direction  (/?.  and  A".),  d',  =  rbi'''"oS. 


0 

00 

00  'GO 

±0  -qS 

90 

24 

53  -48 

0  '21 

128 

03 

37  -66 

0-15 

139 

52 

09-17 

0-28 

191 

28 

17-42 

0  -16 

241 

16 

29-13 

0-35 

250 

34 

52-92 

0  -19 

274 

57 

2738 

0  -20 

282 

51 

27-03 

0  -22 

342 

18 

31  76 

0-43 

July  13  to  August    14,  1895.     45'"'  direction  theodolite  No.  4. 

used  in  XI  positions. 


A.  H.   Buchanan,  observer.      Circle 


Mark  1895 

0     00     00  -QO 

Roan  High  Bluff 

21     02     06-70 

-0-13 

06-57 

Poore 

98     00     40  -56 

+0  -06 

40  -62 

Probable  error  of  a  single  observation  of  a  direction  (D.  and  R.),  e^- 
Consolidated  results  at  Benn. 


-A"-lo. 


Mark  1877 

0 

00 

00  -QO 

18 

Roan  High 

Bluff 

13 

26 

19  -62 

-0-13 

19-49 

-1-25 

18  -24 

19 

Poore 

90 

24 

53-48 

-fo  -06 

55  -54 

+0-18 

53  -72 

20 

Young 
Anderson 

128 
139 

03 
52 

37  -66 
09-17 

+0-01 

37-67 

-0-81 

36-86 

King  * 

191 

28 

17-42 

— 0  -04 

17-38 
+0-23 

Thicketty 

241 

16 

29-13 

Wofford 

250 

34 

52-92 





Paris 

274 

57 

27-38 

Hogback 

282 

51 

27-03 

Mount  Mitchell 

342 

18 

31-75 

*The  line 

Kine  to  Ben 

n  l)ei 

ng  fixed  by 

the  southern  section. 

THE    MAIN    TRIANGULATION. 


i6i 


Abstracts  of  horizontal  directions  at  stations  composing  the  second  or  North  Caroliiia  section  of  the 

triangulation ,  /<Sy6-/8g^ — conti n ued. 

h'ing,  Gaston  County,  North  Carolina.     November  26  to  December  30,  1876,  and  June  17  to  25,  1877. 
50""  direction  theodolite  No.  3.     C.  O.  Houtelle,  ob.server.     Circle  used  in  XI  [)osition. 


Number  of 
directions. 


Objects  observed. 


Results  of  sta- 
tion adjustment. 


AiJjjroxi- 
niate 

l)rot)able 
errors. 


Reduc- 
tions to 
sea  level. 


seconds. 


Corrections      t.--..„i 
from  figure  ^^^^ 
adjustment.  *«==°""*- 


Azimuth  Mark 
Benn  * 

Poo  re 

Anderson 

Young 

WofFord 

Paris 

Thicketty 

Hogback 

Mount  Mitchell 


00 
34 


0(J  'OO 

43  -66 


48     36    08-31 
66    5 1     oS  -80 


85 

284 

293 
296 

307 
345 


53 '17 

19  'GO 

20  '10 

01  -90 

36    45  '89 
51     56-4 


±0  '06 

O  '20 

o-i6 
o  -24 
0-I5 

O  '12 

o  •16 
O  '26 
O  '16 


-o  '06 


43  '60 
-t-O  '02 
08-33 


08-03 


-0-02  53-19 


2-05 


55 '24 


Probable  error  of  a  single  observation  of  a  direction  {D.  and  R 


),  ^,  =  =bo"-69. 


Roan  High  Bluff,  Mitchell  County,  North  Carolina.     October  11  to  24,  1S94.     45*^'"  direction  theodo- 
lite No.  4.     A.  H.  Buchanan,  observer.     Circle  used  in  XI  positions. 


Mark 

24 

Poore 

25 

Benn 

Mount  Mitchell 

Big  Butt 

Chimney 

Big  Knob 

Holston 

23 

Rogers 

0 

00 

00  -00 

34 

17 

14-14 

84 

17 

56-57 

137 

47 

39 '29 

206 

45 

13-80 

246 

oS 

13 '94 

274 

20 

49-02 

303 

26 

14-54 

341 

40 

13  -92 

-o  -01 
-o  -06 


14-13 
56-5: 


— o 
—  I 


1374 
57  7S 


-0-12       14-04 


-o-SS 


13-16 


Probable  error  of  a  single  observation  of  a  direction  ( P.  and  A". 


Rogers,  Graj-son  Count}-,  Virginia.     Jidy  27  to  September  22,  1S94.     45"^"'  direction  theodolite  No.  4. 
A.  H.  Buchanan,  observer.     Circle  used  in  XI  positions. 


26 

27 

2S 


White  Top 

Big  Knob 

Buffalo 

Poore 

Roan  High  Bluff 

Big  Butt 

Holston 


o  00  00  -00 

24  09  36  -83 

194  12  37-64 

266  18  26  -84 

334  18  03  -89 

349  29  28  -or 

35S  23  29  -97 


+0-03  3767  —0-72 
—0-05  26-79  — Q-iS 
+o'i3       04-02         4-0-90 


Probable  error  of  a  single  observation  of  a  direction  (P.  and  RA,  ^■,  =  =bi"-^2. 


*  The  line  King  toBeun  being  fixed  by  the  southern  section. 
4192 — No.  7 — 02 II 


36  -95 
26-61 
04-92 


l62 


I 

II 
III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 


THE    EASTERN    OBLIQUE    ARC. 

Obsen'aiion  cijuations. 

o=^o-io-   (2)+   (4)-   (6)+   (7) 
o=+o-57-   (i)+   (3)-(i6)  +  (i7) 
o=-i-io-    (i)+   (2)^   (7)^   (S)-(i5)  +  fi7) 
o=+o-5i-   (9)+(io)-(i9)  +  (2i) 
o=-4-65— {i3)  +  (i4)-(2o)+(22) 
o=-3-3i-   (8)+    (9)-(i3)^-(^-5)-{2i)  +  (22) 
o=-o-92-    (4)+   (5)+    (6)-(i2)-(26)  +  (27) 
o=-r36-(ii)  +  (i2)-(23)+(24)-(27)+(28) 
o=-3-64-(io)  +  (ii)~-(i8)  +  (i9)-(24)+(25) 

o=~o-5+3-79(3)~i-32(4)-4-o8  (6)+5-i5    (7)-i-o7   (8) -o-48(i5)  +  7-o4(  i6)-6-56(  17) 
o=-5-9+o-i5(8)  +  3"38(9)-3'53(io)-3-29(i3)+5-i6(i4)-i-87{i5)  +  r96(2i)-o-22(22) 
o=  +  i-4-3-8o(5)+5-9i(4)-2>ii   (5)- 1 ■S7(  i4)+3-o7{i5)-r2o(  i6)-o-49(  18)4-3-22  (19) 
-2-73(20) -r6i(23)+3-38(24)-r77(25)-o-68(26)  +  r53(27)-o-85(28) 

o=+7-8-2-55(i)+2-55(2)  +  r32(4)+4-o8(6)-4-o8(7)-3-38(9)+3-38(io)-o-34(i3) 
+0-82(15)— 0-48(17)— 0-41(19)^  2-80(21)  — 2-80(22) 

Nonnal  equations. 


C, 

C2 

c, 

C4 

C5 

C6 

C7 

C8 

C9 

Cio 

C,i 

Cir 

Ci, 

I 

o=— 0  -10 

+  -1 

—  2 

—  2 

+     7 '91 

+ 

5-91 

-  9-39 

2 

+0-57 

+4 

+  2 

-     9-81 

- 

2 -60 

+  2-07 

3 

—  I  -10 

+  6 

—  2 

—   12-30 

+  2  -02 

- 

3 '07 

+  7-'"^S 

4 

+0-52 

+  4 

-2 

-  4 '95 

- 

3-22 

+  9 '97 

5 

—4-64 

+4 

+  2 

+  8-23 

+ 

0-86 

—  2-46 

6 

-3 '31 

+6 

+     o'59 

+  2-47 

+ 

3 '07 

-  7 -82 

7 

—  0  92 

+6 

—  2 

-     2-76 

- 

5 -Si 

+  2-76 

8 

-1-36 

+6 

—  2 

+ 

2-61 

9 

-3 '64 

+6 

+  3 '53 

- 

1-44 

-  3 '79 

10 
II 

-0-5 
-5-9 

+  153-25 

+  0-74 
+68  -74 

_ 

32-12 
15-39 

-36-64 
-17-67 

12 

+  1-4 

' 

+ 

06-92 

+  9-00 

13 

+  7-8 

+87-75 

C,  =  +o-7i9 
C== -0-653 
C3  =  +  i  -096 

C4=  +  I  -080 
C5= +0-838 


Resulting  correlates. 

Cf.  =+0-909 
C,  =+0-726 
Cs  =+0-890 
C,  =  +  1-252 
C,„  = -0-003  86 

Resulting  corrections  to  observed  directions. 


Cii  =  — o  -094  o 
Ci2  =  — o  -009  16 
C,3  =  — o  -loi  5 


(1)  = 

=  -0-185 

(8)  = 

=  +o-i77 

(15)  = 

=  —0-121 

(22)  = 

=+2-052 

(2) 

+0-II8 

(9) 

—0  -146 

(16) 

+0  -637 

(23) 

-0-875 

(3) 

-0  -633 

(10) 

-0-183 

(17) 

+0-517 

(24) 

--  m 

(4) 

—0  -190 

(II) 

+0  -362 

(18) 

-I  -248 

(25) 

+  1  -268 

(5) 

+0  745 

(12) 

+0  -164 

(19) 

+0  -184 

(26) 

—0  -720 

(6) 

-0  -391 

(13) 

-I  -403 

(20) 

-0-813 

(27) 

-0-178 

(7) 

+0-017 

(14) 

+0  -370 

(21) 

-0  -297 

(28) 

+0  -898 

Probable  error  of  an  observed  direction,  o"674 


/i4-66 


zfcO      72. 


THK    MAIN    TRIANGULATION. 


163 


Resulling  angles  and  sides  of  l/ic  second  or  North  Carolina  section  of  the  triang illation. 
No.  Stations. 


Poore 

Buffalo 

Moore 


Young 
Buffalo 
Moore 

Poore 

Buffalo 

Young 

Poore 
Moore 
Young 

Rogers 
Buffalo 
Poore 

Roan  High  Bluff 

Rogers 

Poore 

Benn 

Roan  High  Bluff 

Poore 

King 
Poore 
Young 

Benn 
Poore 
Young 

Benn 
Poore 
King 

Benn 

Young 

King 


Observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
aiiKlcs. 

Spher- 
ical 
excess. 

I,of(.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

27 

18 

38  -87 

H  0-41 

39  -28 

3-51 

4-676   356 

4 

47 

463-13 

57 

5S 

31  '49 

—0  -19 

31  -30 

3-51 

4-943 

028 

7 

87   7.J5  -87 

94 

42 

60  'oS 

-  0  -12 

59-96 

3-52 

5  -013 

257 

0 

103 

CJ99-6 

16 

39 

08-85 

0-12 

08-73 

2-31 

4-676 

356 

4 

47 

463-13 

29 

01 

01  '37 

-0-63 

00-74 

2-31 

4-904 

942 

5 

80 

34'  -98 

134 

19 

57-28 

-f6-i8 

57-46 

2-31 

5-073 

639 

3 

118 

478  -4 

90 

34 

03  -02 

+0-57 

03-59 

5  -01 

5-073 

639 

3 

118 

478  4 

28 

57 

30-12 

+  0-44 

30  -56 

5-01 

4  -758  644 

5 

57 

364  -67 

60 

28 

40  -12 

+0  -76 

40  -88 

5-01 

5  -013 

257 

0 

•03 

099 -6 

63 

15 

24-15 

+0-16 

24-31 

3-81 

4-904 

942 

5 

80 

341-98 

39 

36 

57-20 

+0  -30 

57  -50 

3-8' 

4  -758 

644 

6 

57 

364  -69 

77 

07 

48-97 

+  0-64 

49-61 

3-80 

4-943 

028 

8 

87 

705  -89 

72 

05 

49-12 

+0-54 

49-66 

5-94 

5  -013 

257 

0 

'03 

099 -6 

44 

53 

53-33 

+0-93 

54-26 

5  -95 

4  -883 

517 

2 

76 

474  -60 

63 

00 

34-47 

-0-55 

33-92 

5-95 

4  -984 

727 

I 

96 

544  -40 

52 

37 

00  -09 

+0  -48 

00-57 

4-97 

4  -883 

5'7 

2 

76 

474-60 

67 

59 

37  -23 

^- 1  -08 

38 -3  > 

4-98 

4-950 

523 

6 

89 

232  -62 

59 

23 

36  -24 

—  0-20 

36-04 

4-97 

4-918 

217 

4 

82 

835  -67 

76 

58 

34-05 

+  1-43 

35  -48 

4-23 

4-950 

523 

6 

89 

232  -62 

50 

00 

42  -38 

+  1  -66 

44-04 

4-24 

4-846 

167 

I 

70 

172  52 

53 

00 

52-64 

+0-55 

53-19 

4-24 

4  -864  269 

I 

73 

159-22 

36 

59 

44-86 

+  2-35 

47-21 

4-04 

4  -758  644 

5 

57 

364  -67 

62 

05 

33-02 

-  -0  -32 

32-70 

4-04 

4  -925 

530 

7 

84 

242  -39 

80 

54 

50  -94 

+  1  -28 

52  -22 

4-05 

4  -973 

743 

9 

94 

133  -44 

37 

3S 

44-13 

—  1  00 

43-13 

3  -40 

4  -758 

644 

5 

57 

364  -67 

94 

00 

53-63 

-0-36 

53-27 

3-40 

4-971 

70S 

3 

93 

693  -26 

48 

20 

34-29 

-0  -49 

33-80 

3-40 

4-846 

167 

0 

70 

172-51 

lOI 

03 

24-07 

-0-18 

23-89 

2-95 

4-973 

743 

9 

94 

133  -44 

31 

55 

20  -61 

—0  -04 

20-57 

2  96 

4-705 

136 

5 

50 

715  -oi 

47 

01 

24-71 

—0  -30 

24-41 

2-96 

4  -846 

167 

I 

70 

172  -52 

63 

24 

39  -94 

+0-82 

40  -76 

3  -60 

4-925 

530 

7 

84 

242  -39 

32 

34 

16-65 

+  1-77 

18  -42 

3  -60 

4  -705 

136 

7 

50 

7 '5  03 

84 

01 

09  57 

+  2  -05 

II  62 

3  -60 

4-971 

70S 

5 

93 

693  30 

164 


THE    EASTERN    OBLIQUE    ARC. 


No.  25. 


King 


WoffbrdSl 


Hogback 


iParis 


JPirmacl 


Mduldin 


^-V^ 


iRabi 


"'4. 


Currcthec 


{Skitt 


\Blood 


Grass 


Sat 


Kilometers 

o        10       20 

Statute  Miles 


6.  THIRD  OR  SOUTH  CAROLINA  SECTION  OF  THE  TRI- 
ANGULATION  SOUTH  OF  THE  TRANSCONTINENTAL 
TRIANGULATION,     1873-1877. 

This  section  completes  the  connection  of  the  Kent  Island 
and  Atlanta  bases,  as  already  indicated  in  the  preceding  sec- 
tion. The  results  of  the  adjustment  made  in  Octol)er,  1878, 
are  retained,  omitting  only  the  two  quadrilaterals  lying  be- 
tween the  stations  Butt'alo  and  King,  which  were  included  in 
the  second  section.  The  conditional  equations,  as  well  as  the 
normal  equations,  are  presented  in  full,  leaving  out  the  eight 
triangles  between  the  two  stations  named  above,  as  they  are 
superseded  by  the  present  arrangement.  The  old,  and  less 
convenient,  notation  of  the  corrections  to  the  angles  has  been 
changed,  and  the  order  of  the  presentation  of  the  triangles  has 
been  reversed  .so  as  to  proceed  from  the  northeast  toward  the 
southwest.  The  third  place  of  decimals  in  the  seconds  of  the 
angles  was  dropped  as  unnecessary,  particularli'  since  no 
corrections  for  height  of  .stations  ob.served upon  were  made, 
the  maximum  valueof  this  correction  being  below  o"'i. 

The  .stations  involved  and  their  approximate  heights  are 
as  follows: 

Hogback 

Wofford 

Pinnacle 

Paris 

Mauldin 

Rabun 

Currahee 

Blood 

Skitt 

Relative  weights  to  the  directions  were  introduced  in 
the  same  way  as  had  been  employed  in  the  adjustnient  of 
the  Atlanta  Ixa.se  net.  Referring  to  the  explanation  there 
given,  the  valueof  the  mean  clo.sing  error  of  a  triangle  ( derived 
from  73  cases  in  the  triangulation  connecting  stations  Buf- 


Meters, 

Feet. 

984-4 

3   230 

267-6 

S7S 

I   047-4 

3  436 

626-1 

2  054 

404 -s 

I    3  28 

I   437-7 

4  717 

530-2 

I  740 

T    360-4 

4  463 

632  -7 

2  076 

falo,  Virginia,  and  Kenesaw,  Georgia  )  is 


'V^-^'= 


73 
I '94 


:i    '94 


and  the  probal)le  error  of  a  direction  is  0-674  --7^  =  dzo"-54  ; 

also  the  average  probable  error  of  an  observed  direction  (see 
abstracts)  f,  =  d=o"-i8,  hence  f/— (0-54  )'  —  (o- 18  )°  =  o-255, 
which  was  added  as  a  constant  to  the  square  of  each  observ- 
ing error.  We  have  r-  =  sJ-\-e;  and  the  weight  p—ile'\  in 
order  to  make  the  average  weight  nearly  unity,  the  reciprocal 
was  divided  b>-  0-28.     The  reciprocal  relative  weights  are 

tabulated  farther  on;  the  minimum  value  of  *' or-  iso'5  and 
the  maximum  1-3. 


*  From  the  33  triangles  directly  mvolveil  here  we  ha 


■30  and  the  mean  error  of  a  direction  becomes  ±o"7S. 


I 

I 


THE    MAIN    TRIANGULATION. 


l6^ 


* 


Abstracts  of  horizontal  directions  at  stations  coniprisint:;  the  third  or  South  Carolina  section  of  the 

triajigulation ,  /i'/j-/.?//. 

/\!n<^,  Gaston  County,  North   Carolina.     November  26  to  December  30,  1S76,  and  June    17-25,  1877^ 
50<^"  direction  theodolite  No.  3.     C.  ().  HouUlle,  observer.     Circle  used  in  XI  positions. 


Nuinberof 
directions. 

Objcct.s  ob.served 

Azimuth  Mark 

64 

Benn 

Poore 

Anderson 

Young 

61 

Wofford 

62 

Paris 

Thicketty 

63 

Hogback 

Mount  Mitchell 

Results  of  local  ad- 
justnienl. 


0  00  00  'OtK) 

1  34  43  "656 

4S  36  O.S-3]I 

66  5 1  08  -804 

85  35  53 '167 

284  16  ]  S  -996 

293  54  20  -098 

296  01  01  -905 

307  36  45 '893 

345  51  56-4 


-0  '014 


^,.-„,  menl  of  third 


±0  '06 
O  '20 
o  16 
O  '24 
0-15 
O  '12 

O  tS 
o  -26 

016 


-0  -444 
-I  724 


-rO-413 


Probable  error  of  a  single  observation  of  a  direction  (D.  and  R. ),  <?,  =  =bo"  "69. 

Benn,   Burke  and  Cleveland  Counties,  North  Carolina.     July   25  to  August   22,  1877.     50'' 
theodolite  No.  3.     C.  O.  Boutelle,  observer.     Circle  used  in  XI  positions. 


Final 
.seconds. 


43  '670 


19  440 

18  '374 

46-306 


direction 


Reference  Mark 

Poore 

Young 

Anderson 

65 

King 

Thicketty 

66 

Wofford 

67 

Paris 

68 

Hogback 

Mount  Mitchell 

O      00      00  '000 

90  24  53  '479 

1 28  03  37-657 

139  52  09-167 

191  28  17-424 

241  16"  29-132 

250  34  52  -916 

274  57  27-376 

282  51  27  -027 

342  18  31  -755 

Probable  error  of  a  single  ob.servation  of  a  direction  (D.  and  A'. ),  t',  =  =bi"  oS. 

//()!,' />(?(■/(•,  Greenville  County,  South  Carolina.    August  16  to  September  i,  1S76.    50"' direction  theodo. 
lite  No.  3.     C.  O.  Boutelle,  observer.     Circle  used  in  XI  positions. 


±o-oS 

0  -21 

0-15 

0  -28 

0  -16 

+  0-230 

17    654 

0-35 

0-19 

+  0  -604 

53  -520 

0-20 

-f  0  705 

28-081 

0  -22 

-O-56S 

26  -459 

0-43 

58 

Paris 

59 

Mauldin 

60 

Pinnacle 

Mount  Mitchell 

55 

Benn 

56 

King 

Thicketty 

57 

Wofford 

o  00  00  000 

15  44  50-325 

46  26  55  '104 

158  32  15-94 

20S  54  59-171 

243  34  02  -348 

253  55  03-471 

282  16  22  -064 


±0  -07 
o  -11 
o'  17 
0-44 
0-12 
o-i8 
0-I4 
0-I7 


-0-178 

59  -822 

— 0  -03S 

50  -287 

+1-278 

56  -582 

—0-287 

5S-SS4 

-0  -339 

02  009 

-0-416 


21  -648 


Probable  error  of  a  single  observation  of  a  direction  (/).  and  A\).  c-,  =  zl:o'''  -Si. 


i66 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directious  at  stations  coiiiprising  the  third  or  South  Carotma  section  of  the 

triangiilatioii,  iSj-;-iSjj  -continued. 

IVojford,  Spartanburg  County,  South  Carolina.     July  6  to  August  7,  1876.     50'^'"  direction  theodolite 
No.  3.     C.  O.  Boutelle,  observer.     Circle  used  in  XI  position.s. 


Numberof 
directions. 

Objects  0 

Thicketty 

54 

King 

50 

Paris 

51 

Pinnacle 

52 

Hogback 

Mount  Mitchell 

53 

Benn 

Results  of  local  ad- 
justineut. 


O 

22 

226 

235 
264 
300 

33S 


GO  '000 
08  '507 
58  -853 

59"i37 
27     49  '062 
04     42 
50    02  -589 


'^l„??  meutof  third 


dzO  '09 
0-I4 
o-i6 
o  '16 
o  -26 


+0  -580 
+0  -635 

-o  -656 

+0  -862 


0-I5 


1-343 


Probable  error  of  a  .single  observation  of  a  direction  ( /).  and  R.  ] 


-±o"  'gS. 


Final 
seconds. 


09  "087 

59  -488 
58  -481 

49  "924 
01  '246 


Pinnacle,  Pickens  County,  South  Carolina.     August  25  to  September  8,  1875.      50'"'  direction  theodo- 
lite No.  3.     C.  O.  Boutelle,  observer.     Circle  used  in  XI  position,'?. 


38 

Paris 

39 

Mauldin 

40 

Currahee 

41 

Rabun 

36 

Hogback 

37 

Wofford 

O  00  00  "000 

48  46  48 '017 

117  37  44 '518 

153  07  06  -908 

321  u2  43-547 

347  34  20  -804 


iO  'lo 

o  -17 

O  •\2 

o  •14 

O  '21 

o  '17 


+0  -258 
+0  -032 

+0  -269 

+0  -856 

-o  -887 

--0-637 


Probable  error  of  a  single  observation  of  a  direction  [D.  and  R.  ),  t'i=  ±:o"-92. 

Paris,   Greenville  County,  South  Carolina.      September    16  lo  November  20,    1875.      y^"'' 
theodolite  No.  3.     C.  O.  Boutelle,  observer.     Circle  used  in  XI  positions. 


00  -258 
48  -049 
44  787 
07  -764 
42  -660 
20-167 

direction 


o  00  00  -000 

94  35  47  "974 

109  45  43  "oSo 

1 15  36  49  -945 

142  59  15  -298 

144  27  28-012 

15S  30  21-824 

229  12  08-277 

30S  16  00-933 

314  06  42-296 

343  20  09  -423 
Probable  error  of  a  single  observation  of  a  direction  {D.  and  R. ),  i'i=  ±0^-93. 


45 

Pinnacle 

46 

Hogback 

Propst 

47 

Beiin 

Thicketty 

48 

King 

49 

Wofford 

Azimuth  Mark 

42 

Mauldin 

43 

Currahee 

44 

Rabun 

±0  -06 

-0  -079 

59 '921 

0  -19 

fo  -020 

47  -994 

0-17 

0-09 

+  1-183 

51-128 

0-17 

0  -21 

--0-I55 

27  -857 

0-2I 

+0  -304 

22  -128 

0-I7 

0  -14 

-0-755 

■  00  - 1 78 

0-18 

-0  -947 

41  -349 

0-16 

+0  -320 

09  743 

THE   MAIN   TRIANGULATION. 


167 


Abstracts  of  horizontal  direclions  at  stations  comprisinf:;  the  third  or  South  Carolina  section  of  the 

trianjj^iilation ,  1R73-  /Hyy — coiiti  iiued . 

JMatttdin,  Pickens  County,  vSouth  Carolina.      December  S  to  14,  [875.     50""  direction  thecjdolite  No  .3. 
C.  ().  Boutelle,  observer.     Circle  used  in  XI  positions. 

,,,•,„       ,      ^     ,,  Results  of  local  ad-       '^'''*/'l''A"?'''"'      from  adjust-  Final 

Objects  observed.  justment.  Trror'         ment  of  third  second.s. 


Number  of 
direction.s. 

I 

33 

Pinnacle 

34 

Hogback 

35 

Paris 

31 

Currahee 

32 

Rabun 

secliou. 

0 

/ 

// 

// 

n 

n 

0 

00 

(XI  "CXX) 

±0  '07 

t-O  '022 

00  -022 

61 

33 

5'  -967 

o-i8 

-0-598 

51    369 

79 

29 

1 2  -823 

o-i6 

+  1  -215 

14  -038 

267 

13 

16-950 

0  -12 

-I-0-II2 

17-062 

307 

25 

59  -062 

Q-II 

-0  -678 

58  -384 

Probable  error  of  a  single  observation  of  a  direction  {D.  and  R.  ),  ^,=  d=o"-77. 

Ratnm,  Rabun   County,   Georgia.      July   27   to   August  5,    1875.      50'"'    direction   theodolite    No.    3. 
C.  O.  Boutelle,  observer.     Circle  used  in  XI  positions. 

o  /  // 

o     00      00  -(XX) 

51     4'^^    33 '214 
80    53     21  -496 

89     5'     56-194 
no     31      24-370 

304     59    5>'^'ii9 
315     13     "1  "555 
32S    05     38 -177 
Probable  error  of  a  single  observation  of  a  direction  (  P.  and  R 

Currahee,  Habersham  Count}-,  Georgia.     September  17  to  November  21,  1874.      50'"'  direction  theod- 
olite No.  3.     C.  O.  Boutelle,  observer.     Circle  used  in  XI  positions. 


Walhalla 

28 

Currahee 

29 

vSkitt 

Yonah 

3" 

Blood 

25 

Pinnacle 

26 

Paris 

27 

Mauldin 

±0  -08 

0  -20 

-0-351 

32-863 

0-17 

-f  I  -023 

22-519 

0-23 

0-31 

-0  -354 

24-016 

0-15 

—0  -987 

57  •132 

0  -  r  2 

—0  -220 

01  -535 

0-14 

-0  -S30 

39-007 

.),  i\  = 

±0^-85. 

► 


Azimuth  Mark 

22 

Pinnacle 

23 

Paris 

24 

Mauldin 

18 

Sawnt^ 

19 

Skitt 

Yonah 

20 

Blood 

21 

Rabun 

O  00  CX)  -QOO 

9  3>  57 '621 

26  01  CX3-177 

27  54  22  -374 
209  40  29  -255 
229  04  06  -507 

254  59  47  703 

255  14  09-621 
331  49  ,So-24S 


±0-07 
o  -11 
0-I4 
0-14 
0-14 
o  -16 
0-25 

0-I5 
0-17 


—0  -042 

57  -579 

+0  -0S5 

00-262 

+0  -369 

22  -743 

-0  -552 

28  -703 

-0-432 

06  075 

+0  -661 
— o  -090 


10-2S2 
50-158 


Probable  error  of  a  single  observation  of  a  direction  (  /•>.  and  A'. ),  ^,  =  =t  o"-So. 


i68 


I 


THE    EASTERN    OBLIQUE    ARC. 


Abslracts  of  horizontal  directions  at  stations  comprising  the  third  or  South  Carolina  section  of  the 

triangulation,  i8jj-i8jj — continued. 

Blood,  Union  County,   Georgia.     June  30  to  July  15,  1S75.     50'^™  direction  theodolite  No.  3.     C.  O. 
Boutelle,  observer.     Circle  used  in  XI  positions. 


Corrections 


Number  of 
directions. 

( 

Yonah 

15 

Skitt 

16 

Sawnee 

17 

Grassy 
Cohutta 

13 

Rabun 

14 

Currahee 

Objects  observed. 


justment. 


O      GO      00  '000 

23     53     12-312 

Si     25     II  -718 

113     23     06  •2S0 

167     15     34  '393 
307     42     15  -079 
355     23     50  761 
Probable  error  of  a  single  observation  of  a  direction  ( /).  and  R.  \ 

Skitt,  White  County,   Georgia.     August    14   to    25,    1S74.     50'™  direction   theodolite    No.  3.     C.  O. 
Boutelle,  observer.     Circle  used  in  XI  positions. 


probable 
error. 

from  adjust- 
ment of  third 
section. 

Final 

seconds. 

// 

// 

// 

±0  -qS 

0-I7 

-0  -403 

II  -909 

0  '19 

+0  -383 

12  -lOI 

0-22 

+0  •480 

06  -760 

o-!9 

0-I4 

—0  '221 

14  -858 

0-I5 

-0-195 

50  -566 

e.),^.= 

±o"-94. 

Yonah 

II 

Rabun 

12 

Currahee 

8 

Sawnee 

9 

Grassy 

10 

Blood 

0 

00 

GO -000 

zbo  -09 



33 

56 

23-941 

0  -16 

-0-105 

23  -836 

82 

05 

53  '452 

0-15 

-(-0-510 

53  '962 

230 

31 

07  -207 

0-17 

—0-009 

07-198 

264 

50 

54  -066 

0  -14 

—(  -304 

53  762 

319 

45 

17-372 

0-I5 

—0  -092 

17  -280 

Probable  error  of  a  single  observation  of  a  direction  (£>.  and  J?.),  t',=  ,rb  o"-84. 

Sawnee,  Forsyth  County,  Georgia.  October  7  to  November  12,  1873,  siif^  November  26  to  December 
4,  1873.  75""  direction  theodolite  No.  i  and  50="  direction  theodolite  No.  3.  C.  O.  Boutelle, 
observer. 

Corrections 

LlOllb  K.CbUlLlU^ 

from  base  direc- 

Tif.t  afl-  timi<i 

error. 


Number  of 
directions. 

Objects  observe 

Azimuth  Mark 

Alcova 

I 

Grassy  * 

2 

Blood 

Yonah 

3 

vSkitt 

4 

Currahee 

Results  of  station 
adjustment. 


Approxi 

justment. 


tions  R^uUrng      ^^^i^^.    pi„,, 


ment  of  3d    seconds, 
section. 


O  00  00  -QOO 

5  59  50  -203 

191  04  26-154 

240  44  00  -564 

263  1 1  38  -044 

273  57  55  -373 

2S6  09  07  -228 


±0  -09 
o  -24 

O  "22 

o  -24 

0-31 
0-32 
O  -22 


+  0-005 
+0  -005 

-o  -244 

+0-005 
+  0  -005 
+0  -005 
+0  -005 


00  -005 
50  -208 
25-910 
00  -569 

38  -049 

55  '378 
07  -233 


-o  -109       25  -801 
-o  -800      01  -369 


-0-124     55-254 

-o  -455       06  -778 


Grassy,   Pickens    County,  Georgia.     July    13  to  31,  1874.     50'"'  direction    theodolite    No.    3.     C.   O. 

Boutelle,  observer. 


o  00  00  "OtX) 

131  59  17 '050 

183  15  38  -960 

261  37  28  -061 

297  13  10  -620 


7 

Sawnee  * 

Johns 

Cohutta 

5 

Blood 

6 

Skitt 

// 

// 

// 

// 

// 

±0-07 

+0-228 

00-228 

—0  -097 

00-131 

0-26 

o-iS 

—0  -032 

38  -928 

0-15 

-0  -032 

28  -029 

-I  -338 

26  -691 

0-16 

—0  -032 

10  -588 

+  1  -532 

12  -120 

*This  direction,  which  is  now  considered  as  fixed,  and  hence  not  liable  to  a  further  correction,  was  formerly  treated 
as  subject  to  correction. 


THE   MAIN   TRIANGULATION. 


169 


I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 

XIV 

XV 

XVI 

XVII 

XVIII 

XIX 

XX 

XXI 

XXII 

XXIII 

XXIV 

XXV 

XXVI 

XXVII 

XXVIII 

XXIX 

XXX 

XXXI 

XXXII 
XXXIII 
XXXIV 


Observation  equations. 

o=  +  r938-(6)  +  (7)-(i)-r(3)     (8)^(9) 
o=-2-247-(5)  +  (7)--(i)-|-(2)-(i6)  +  (i7) 
o=- 3 ■964^(5)-!  (6)-(9)+(io)-(i5)-.  (17) 
o=-o-535-(2)4(4)-(i8)+(2o)-(i4)  +  (i6) 
0=i073i-(3)  +  (4)-{i8)-}-(r9)-(i2)  +  (8) 
o=+o727  -(2o)  +  (2i)-(28)  +  (3o)-(i3)  +  (i4) 
o=  +  i-572-  (io)  +  (ii)--(29)-|-(3o)-(i3)  +  (i5) 
o=-i-27o  -  (25)  +  (28)~(2i)  +  (22)      (40)+  (41) 

0=+I-5I2-(27)f(2S)-(2l)  +  (24)-(3l)-i-(32) 

o=~o-559~-(39)  +  (4o)-(22)  +  (24)-(3i)  +  (33) 
o=-r3ii-(26)+(28)-(2i)  +  (23)-(43)-r(44) 
o=-i -195"  (23) +(24) -(31)  + (35) -(42) -J  (43) 
o=-i-6i6--(36>+(39)-(33)K34)-(59)+(6o) 

o=-2-727-(34)-f(35)-(42)4-(46)-(5S)  +  (59) 
o=+o-oi3-(37)+(38)-(45)  +  (49)-(5o)  +  (5i) 
o=-3-463-(57)  +  (6o)-  (36)-|  (37)  -  (5' )  +  (52) 
0= -0750- (57)+ (58)  (46)-(49)-(5o)  +  (52) 
o=  +  2755-(47)  +  (49)-  (50) +  (53)-(66)  t  (67) 
o=+3-5o6- (55)+(57)-{52)n  (53)-(66)  +  (6S) 
o=-2-i24-(56)  +  (58)--(46)  +  (48)~(62)  +  (63) 
o=4o-390-(56)  +  (57)^(52)  +  (54)-(6r)-f(63) 
o=-i-867-(65)  +  {66)-(53)+(54)--(6i)-f  (64) 
o=+o-8o5-(7i)  +  (65)-(64)  +  (69)-(8i)^(S2) 
o=  +  2-397-(8o)  +  (82)-(7i)  +  (72)~(74)+(75) 
o=-3-26o-(8o)  +  (8i)-(69)+(7o)-(73)+(75) 
o=-ro4i-(79)  +  (So)-(75)  +  (77)-(83)  +  (84) 
o=+o-8o2-(86)  +  (88)-(78)H-{79)-(84)  +  (85) 
o=+o-905-(86)  +  (87)-(76)  +  (77)-(83)  +  (85) 
o=-o-oi -0-153(1) -0-026(3) -(-o-i79( 2) -o'3o8 (8) +0-456(9) -0-148 (10 1^0-337(16) 

-o-335(i7)-o-oo2(i5) 
o=+o-5o+ 1 -295(3) --0-321  (2)-o-974(4)-o-i34(  16)  4-0-521  ( 15 )-o-3S7(i4)-o-598(iS) 

+  0-975(19) -0-377(20) 
o=- 1 -53-0-336  (15) +0-387(14) -0-05 1  (13) -0-425  (19) -.-0-377(20)— 0-048(21) 

+o-749(  29)  -0-370(30)  -o-379(  28) 
o=+o-65+o- 142(21) ^0-634(22) +0-492(24) +  0-024(28) -0-945(27)^0-921(26) 

-0-082(40) +  0-266(39) -0-184(38)  I  0-300(44) -o- 166(45) -0-134(42) 
o=  +  2-i2-o-634(22)-5-749(24)46-383(23) -0-082(40)  .  o-266(39)-o-i84(38) 

4  2-o57(43)-o-i66(45)     1-891(42) 
0=40-46+0-675(25)  I  0-493(27)      i-i68(26)+o-i62(32)-o-2oi(33)-  0-039(35) 
0-703(44)  fo-537(45)  r  0-166(42) 


N.  B. — The  6  equations,  XXIII  to  XX\'III,  refer  to  the  2  quadrilaterals  iu  the  old  work,  of  which 
no  further  use  is  made  here.  The  nuniViered  corrections  are  as  follows:  at  AY//",  Poore  (691,  Vouiiji 
(70);  at  Beun,  Poore  (71),  Young  (72);  at  }'o/ini;.  King  (73),  Henn  (74),  Poore  (75),  Huflfalo  (76), 
Moore  (77);  at  Poore,  Buffalo  (78),  Moore  (79),  Young  (80),  King  (Si),  Benn  (82);  at  Moore,  Young 
(83),  Poore  (84),  Buffalo  (85);  and  at  Hiiff'alo,  Moore  (86),  Young  (87),  and  Poore  (S8). 


I/O 


XXXV 

XXXVI 

XXXVII 

XXXVIII 

XXXIX 

XL 

XLI 


THE   EASTERN    OBLIQUE   ARC. 

Observation  equations — continued. 

o=:-o-98+o-i84(39)-o'445(38)+o-26i(36) +0-039(33) -o-6i2(35)-o-65i  (34) 

+0-200(60) -0747(59) +0-547(58) 
o=+2-6o— 0-694(38) -0-26  r(36)+o-955(37) -0-200(60) -^0-246(58) -0-046(57) 

+  '■319(51)-! '053  (50) -0-266(52) 
o=-2-34-o-445(46) -0-103(49) +0-548(47) -o-266(5o)+o-325(52) -0-059(53) 

+  i-5iS(67)-i-i84(68)-o-334(66) 
o=  +  2-i7-o-o74(46)— 0-103(49) +0-177(48)— o-266(5o)+o-325(52)— 0-059(53) 

+0-339(68)  -0-334(66)  ~o-oo5(65)+o-863(62)-i-oi7(63)+o-i54(64) 
o=+3"o5— 0-103(46)— 0-738(49) +0-841  (48)— 0-046(58) +0-309(57)— 0-263(56) 

+  i-24o(62)-o-488(63)-o-752(6i) 
o=— 0-78-0- 174(64) +0-196(69)— 0-022(70)— 0-353(82)^-0-338(81) +0-015(80) 

+0-516(74) -0-329(73) -0-187  (75) 
o=+o-20-o-i07(8o)  -0-408(78)  +o-5i5(  79)  -o-o48(  75)  +o-704(  76)  -o-656(  77) 

-o-i32(88)+o-379(87)-o-247(86) 
The  last  two  equations  refer  to  the  quadrilaterals  already  disposed  of. 


Normal  equations. 

C2        C3        C4        C5        C6        C7        Cs        C9       Cio       Ci,       Ci 


C13      C14       C15       Ci 


0=4-1-938 

o=— 2-247 
0=^3-964 
0  = -0-535 
o  =  +o-73i 
o=+o  727 
0= +  1-572 
o=  — I  -270 
o=  +  t  -512 
o=-o'559 
0=  I -311 
o=-i-i95 
o=  — I  -616 
o=— 2-727 


H5-3   +1        -2 

+  5-2  +2- 

+6- 


+6- 


+  2-1 
+64 


+6-2  +2-2 
+6-2 


Ci=  C16 


+6-0  +2       —2       +2 

+  5-9  +2       +2       +2 

+5-9  +2 

+6-0  -2 
+6 


Normal  equatioiis—conXxwA^Ci. 

C18  Cr<)  Cso  C21  C22  C25 


+2 

+6       -2 

+5-9 


C25 


C26 


-1-9 


C23 


15 

o=+o  -0]3 

+  5-9 

—  2 

+  2-r 

+  2-1 

16 

o=-3'463 

+  6-2 

+  2-1 

2  ■  1 

2-1 

17 

0= -0-750 

+6-1 

+  2-1 

-2  -I 

+  ■■9 

-2-1 

18 

o=  +  2-755 

+  6-1 

+  2 

-2 

19 

o  =  +  3-5o6 

+6-2 

+  2-1 

—  2 

20 

o=  — 2-124 

+  6-0 

+  2 

.... 

21 

0= +0-390 

+6-1 

+  2 

22 

o=  — I  -867 

+  6-1 

-2  -I 

23 

0= +0-805 

+  6-2 

+  2-1 

—  2 

24 

o=  +  2-397 

+6-1 

+  2 

-2 

25 

o  =  — 3-260 

+6 

—  2 

36 

0  =  —  I  -04  ! 

+6 

—  2 

+2 

27 

0= +0-802 

+6-2 

+  2-2 

28 

0= +0-905 

+6-4 

THE   MAIN   TRIANGULATION. 


171 


C29 


C3t 


Noniia/  equations  —  com plclec' 

C32  C33  C34  C35 


C36 


Cj3 


Cji 


I 

+0 

8067 

+  1 

•6835 

, 

2 

— 0 

4321 

— 0 

■2191 

3 

— 0 

9705 

—  0 

■5210 

+0 

■3360 

4 

+0 

1401 

-0 

•2443 

— 0 

'0100 

5 
6 

•2742 

■1819 
•0100 

■4250 

'0440 

—  0 

+0 

+  0 

•ilSo 

7 

+0 

1460 

+0 

•5210 

- 1 

•4780 

8 

^0 

■4270 

—  0 

■5700 

-o'5520 

— 0 

6750 

9 

-0 

•4270 

+  1 

•3190 

-57490 

—  0 

3472 

+0 

77S0 
•739" 

-5 '4630 
+  4  '3260 

1809 

1489 

II 

— 0 

•4270 

—  0 

+  0 

4650 

12 

+0 

■6260 

-8-1840 

—  0 

1270 

+0 

6120 

13 

+  0 

•2660 

+  o'266o 

+  0 

l8oq 

+  0 

1578 

+0-0871 

14 

+  0 

•1340 

+  1  '8910 

—  0 

1270 

+0  -0237 

-02214 

-0-4450 

—0  -0740 

— 00616 

Normal  equations. — completed. 

C35  C36  C37  C38 


C3') 


C4 


15 

-0-0162 

—  0-0162 

-0  -4833 

—0  -4005 

+0-7924 

+0-1527 

+0-1527 

-o-8n8 

16 

—0-0871 

-0-5235 

+0-3575 

+0-3575 

-0-3090 

17 

+0  -4923 

+  1-0278 

+0  -9552 

+0-5842 

-1-0592 

• 

18 

+ 1 '0530 

+ 1  -6043 

+o'4277 

-o-SiiS 

19 

+0  -2466 

- 1  '3849 

+0-2904 

+0-3090 

20 

+0  -4923 

+0-2214 

+0  -4450 

-1-6113 

-0  -4783 

21 

+0  -2466 

-0"3575 

-1-3745 

+0  -8360 

22 

-0-2750 

—0-1006 

+0-7520 

-0-1914 

23 

-0-1744 

-0-3036 

24 

—  I  -0710 

+0  0590 

25 

+0  -2470 

+0  -0590 

26 

+0-2020 

- 1  -2300 

27 

+  1-0627 

28 

-0  6335 

Normal  eguatioji'^ — completed. 


C29 


C,r 


C35 


C36 


C33 


C40 


29 

o=— o'oi   +0-6096   -0-1532  +0-0007 

30 

o=+o-50 +52265  -0-8813 

31 

o  =  -i-53                                   +1-4592  -0-0023 

32 

o=+o-65                                                       +2-6467   -2-0404  -1-8550   +0-1226   +0-II49 

33 

o  =  +  2-i2                                                                       +S2-1355   -0-3941   +0-1226  +0-II49 

34 

o=+o-46                                                                                          +2-9057  +0-016S 

35 

o=-o-98 +1-9540  +0-2S41   -0-0226 

36 

o=  +  2-6o                                                                                                                     +4-4434  +0-1S50  +0-1S50  -00244 

37 

o=-2-34                                                                                                                                              +4-8588  -0-0949  +0-1295 

38 

o=  +  2-i7                                                                                                                                                               +2-2S52  +1 -8214 -ooi<)5 

39 

o=+3-05                                                                                                                                                                                 +3-8955 

40 

o=-o-7S +0-7207+00074 

41 

o  =  +o-2o                                                                                                                                                                                       +r62S3 

1/2 


THE    EASTERN    OBLIQUE    ARC. 


Resnltiuo;  I'alues  of  correlates. 


C, 
C. 
C3 

C4 
Cs 

C6 

Cs 

C9 

C.o 


=  f  I 
=+0 

=  — o 

=+0 

=  — o 

=  i-o 
=  — o 

=+I 


•330  62 
■137  00 

•200  89 

•694  67 

■510  27 

■263  S3 
•105  40 

•S55  96 

•722  30 
•099  17 


C„  = 

C.3  = 

C.4  = 

C,6  = 

C,8  = 
C,9  = 


: +0-248    30 

:-o'488  74 
^  +  1  '13'  56 
^  +  1  "433  16 
: +0-036  14 

:— 0-057     86 

:+0-223    61 

-0-795  56 

: +  0-286  98 
:  +  O  -840    26 


C,i  =  -o-i42  55 
0^,= +0-723  09 

C23= +0-957    84 

C.4=--i  -151  53 
C.5=  +  i  -412  85 
C,6= +0-424  81 
C=7  = +0-139  80 
C^8=— 0-302  7 

C25=+2  -692    01 

C3„=+o-6i4  15 


C3i  =  +I 


-33" 


— O 

C34=-0 
C35=+0 
€36=  "O 
C37  =  +0 
C,8=+0 
C3,=  -I 
C40=-0 

C4i  =  -o 


■224  74 
■214  82 
■102  086 
■193  85 
■454  91 
■56S  89 
•946  19 
■934  10 
■362  70 
■598  29 
016  91 


(I) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 

(9) 
(10) 

(II) 

(>2) 

(13) 
(14) 
(15) 
(i6) 

(17) 
(18) 

(19) 
(20) 
(21) 
(22) 


0-5 
I  -I 

I '3 
I  -r 
I  -o 
I  -o 

0-5 
I  -o 
I  -o 
I  -o 
I  o 
I  -o 
I  -o 
I  -o 
I  -o 
I  -o 
I  -I 
I  -o 
I  -o 
I  -o 
I  -o 
I  -o 


Reciprocals  of  weights  and  resulting  corrections  to  observed  directions. 
I 


— o  -1091 
+0  -7998 
-0-1235 
-o  -4552 
-I  '3379 
+  1  "5315 
— o  -0968 
— o  -0088 
-o  -3040 
—  o  -092 1 

-0-1054 
-f  0-5103 

— o  2209 
-o  -1946 
— o  -4032 

+0  -3826 
+0  -4797 
-0-5517 

-o  -4320 
+0  -6610 
— o  -0898 
— o  -0423 


(23 
(24 
(25 
(26 

(27 
(28 

(29 
(30 

(31 
(32 

(33 

(34 
(35 
(36 
(37 
(38 
(39 
(40 

(41 
(42 
(43 
(44 


P 


I  -o 

I  -o 

I  -o 

I  -o 

I  -o 

I  o 

I  -o 

I  -2 
I  -o 
0-9 
0-9 

(  I  -o 

I  -o 

I  -I 

I  -o 

0-9 

I  -o 

I  -o 

I  o 

I  -o 

I  -o 

I  -Q 


-t-o  -0854 

+0  -3693 

-o  -9868 
— o  -2197 

+0  -8298 
-0-3512 

+  1  -0227 

-o  3537 
+0  -1119 
-o  -6783 
4  o  -0219 
-o  -5978 

+  1  '2153 
-0-887I 
-  o  -6373 
+0-2581 
+0-0318 
+0  -2692 
+0  -8560 
-o  -7548 
— o  -9470 
+0  -3201 


(45 
(46 

(47 
(48 
(49 
(50 
(51 
(52 
(53 
(54 
(55 
(56 
(57 
(58 

(59 
(60 
(61 
(62 
(63 
(64 
(65 
(66 


J 

0-9 
I  -o 
0-9 
I  -I 
0-9 
I  -o 
r  -o 
r  T 
I  -Q 
I  -o 
I  -o 
I  -o 
I  -o 
0-9 
I  -o 
I  -o 
I  -o 
I  -o 
I  -o 
I  -o 
I  -o 
I  -o 


— o  -0789 

+0  -0195 
+1  -1827 
-0-1545 
+0  -3038 
+0  -6347 

-  o  -6564 

+0  -8621 
- 1  '3426 
+0  -5805 

— o  -2870 

-o  -3393 
—0-4162 
— o  -1780 
— o  -0382 

+1-2785 
+0  -4442 

-I  7239 
+0-4127 
+0  -0145 

+0  -2301 
+0  -6036 


(67) 

(68) 

(69) 
(70) 
(71) 
(72) 
(73) 
(74) 
(75) 
(76) 
(77) 
(78) 
(79) 
(80) 
(81) 
(82) 
(83) 
(84) 
(85) 
(86) 

(87) 
(88) 


—  V 


-I 

+0  -7048 

-I 

-0  -5683 

-0 

—0-5722 

-0 

+  1  -4260 

-I 

+0-2130 

-0 

-I  '1515 

-0 

—  I  -2160 

-0 

+  0  -8429 

-0 

— 0  -0508 

■0 

+0  -2908 

-0 

+0-1331 

•0 

—0-1329 

•0 

-0  -2938 

-0 

+0-1564 

•0 

+0  -2528 

-0 

+  0-0175 

•0 

—0  -1220 

•Q 

+0  -2850 

•I 

-0  -3089 

•I 

+0-1893 

-2 

—  0-371 1 

-0 

+O-I42I 

THR    MAIN    TRIANGULATION. 


^73 


A'fsu//h/i^r  angles  and  sides  of  tlw  third  or  South  Carolina  section  of  the  triangnlalion. 


No. 


Wofford 
Beim 

King 

Hogback 

Beiiii 

King 

Paris 
Benn 
King 

Wofford 

Hogback 

King 

Hogback 

Benn 

Wofford 

Paris 
King 
Wofford 

Paris 

Hogback 

Benn 

Paris 

Hogback 

King 

Paris 
Benn 
Wofford 

Paris 

Hogback 

Wofford 

Pinnacle 
Hogback 
Paris 

Pinnacle 
Hogback 
Wofford 


Observed 
.angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher 

•cal 
exces.s 

0 

/ 

// 

// 

// 

// 

43 

35 

05-92 

+  1  -92 

07  -84 

2-64 

.59 

06 

35  '49 

fo38 

35  -87 

2-65 

77 

18 

24  -66 

-0-43 

24-23 

2-65 

34 

39 

03-18 

-0-05 

03-13 

3-10 

91 

23 

09  '60 

-o-8o 

08  80 

3-09 

53 

57 

57l(> 

—0  -40 

57  -36 

3-10 

28 

50 

3S  -07 

-1-34 

36-73 

4-15 

83 

29 

09-95 

-1-0  -47 

10  42 

4-15 

67 

40 

23  -56 

+  1-74 

25  -30 

4-15 

117 

57 

19-44 

-0  -2S 

19  -16 

1-89 

3'S 

42 

19-72 

--0  -08 

19-64 

1-89 

23 

20 

26  -90 

-0-03 

26 -87 

I  -89 

73 

21 

22  -89 

-0-13 

22  -76 

2-34 

32 

16 

34-11 

-I -■■7 

32  94 

2-34 

74 

22 

13-53 

—  2  -21 

II  -32 

2  '34 

14 

02 

53 -Si 

+  0-46 

54-27 

0-93 

9 

37 

61  -lo 

-2-17 

58-93 

0-94 

156 

19 

09-65 

-0-05 

09  -60 

0-93 

21 

01 

01  -97 

+  \  -16 

03-13 

0-82 

151 

05 

00-83 

-j-O  -II 

00  -94 

o-Si 

7 

53 

59-65 

-I  -27 

58  -38 

0  -82 

49 

5' 

40-04 

— o-iS 

39-85 

I -87 

116 

25 

57-65 

+0-16 

57-81 

1-87 

13 

42 

25 -So 

+2-14 

27-94 

1-87 

42 

53 

31 -88 

-0  -88 

31  -00 

2-44 

24 

22 

34-46 

+  0-I0 

34-56 

2-44 

\\2 

44 

03-74 

—  I  -98 

01  -76 

2-44 

63 

54 

33  -85 

+0  -28 

34-13 

0  -92 

77 

43 

37  -94 

+0-24 

38-18 

0  -92 

3^^ 

21 

50-21 

+  0-23 

50  -44 

0  -91 

3S 

57 

16-45 

+  I-I5 

17  -60 

0-74 

46 

26 

55-10 

-^i  -46 

56-56 

0-75 

94 

35 

47-97 

—0  'lO 

48  -07 

0-74 

26 

31 

37  -26 

+0-25 

37-51 

1  '23 

124 

10 

33  -04 

+  1  -70 

34  -74 

I  -23 

29 

17 

49-92 

+  1  -52 

51  -44 

I  -23 

I-og. 
distances. 


4-705 
4  -800 

4-855 

4  -705 
4-950 

4  -858 

4-705 
5-018 

4-9S7 

4  950 
4-800 
4  -602 

4  -855 
4  -602 
4-858 
4  -800 
4-638 
5-018 

4  -858 
4-987 
4-441 

4-950 

5  -018 
4-441 

4  -S55 
4  -638 
4  -987 
4  -602 
4  -638 
4-441 

4  441 
4-503 
4-641 

4-602 
4-869 
4-641 


.'36  6 

210  3 
9(ji  2 

136  6 
231  9 
124  o 

136  6 
914  I 

882  5 

231  9 
210  3 
019  6 

901  2 
019  6 
124  I 

210  3 
655  1 
914  I 
124  o 
8S2  4 
543  7 
231  S 
914  o 
543  7 
901  2 

655  1 

8S2  5 

019  5 
655  o 
543  7 

543  9 
290  4 

697  6 
019  6 
757  3 
697  5 


Distances 
in  meters. 


50  715  02 
63  I  26 -29 

71  763  10 

50  715  -02 
89  172-70 

72  131  -33 
50  715-02 

104  451  -4 

97  248-41 

89  172  -70 
63  126  29 
39  996  -28 

71  763-10 
39  996  -28 

72  131  -35 

63  126-29 
43  516-62 
104  451  -4 

72  :3i  '33 
97  24S-39 
27  640  -36 

89  172  -67 
104  451  -4 
27  640  -36 

71  763-10 
43  516  62 
97  248-41 

39  996  27 
45  516-61 
27  640-36 

27  640-37 
31  863  27 
43  S22  -55 

39  996  -28 
74  0S9  -61 

43  822  -53 


174 

Ixesnliiug  angles  and  sides 


THE    EASTERN    OBLIQUE    ARC. 


13 


14 


15 


16 


17 


iS 


19 


Pinnacle 

Wofford 
Paris 

Mauldin 
Hogback 
Paris 

Mauldin 
Pinnacle 
Hogback 

Mauldin 
Pinnacle 
Paris 

Rabun 
Pinnacle 

Paris 

Rabun 

Paris 

Mauldin 

Rabun 

Pinnacle 

Mauldin 

Currahee 
Pinnacle 
Paris 


f  Cur 
\    Pin 


urrahee 
nacle 
IMauldin 


2i 


Currahee 

Paris 

Mauldin 

Currahee 

Rabun 

Pinnacle 

Currahee 

Rabun 

Paris 


he  1/ 

u-d 

or  Soitt/i  Carolina 

section 

of  the  tr 

iangulation — continued. 

observed 
angles. 

Correct- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log. 
distances. 

Di.stances  in 
meters. 

0 

/ 

n 

// 

// 

// 

12 

25 

39  '20 

+0-90 

40  -10 

0-43 

4  -638 

655  I 

43 

516-62 

9 

03 

60-28 

-1-29 

58-99 

0-43 

4  -503 

290  4 

3' 

863  -27 

15S 

30 

21  -82 

+0-38 

22  -20 

0-43 

4  -869 

757  3 

74 

0S9  -61 

17 

55 

20  -86 

+  1  -81 

22  -67 

0-31 

4-441 

543  5 

27 

640  -35 

15 

44 

50  -32 

+0-14 

50-46 

0  -32 

4  -386  965  5 

24 

376-17 

146 

'9 

47-04 

+0-78 

47  -'^2 

0-32 

4-697 

196  I 

49 

796-18 

61 

33 

51  '97 

-0  -62 

51  -35 

0-94 

4-641 

697  4 

43 

822  -52 

87 

44 

04-47 

+0  -92 

05-39 

0-94 

4-697 

196  3 

49 

796-21 

30 

42 

04  -78 

+  1  -31 

06  -09 

0-95 

4  -405 

586  3 

25 

444  -05 

79 

29 

12-82 

^-I  -19 

14  -01 

0-52 

4  -503 

290  3 

31 

863  -26 

48 

46 

48  -02 

-^-0  -23 

47-79 

0-52 

4  -386  965  6 

24 

376-18 

51 

43 

59 '07 

+0-68 

59  -75 

0-51 

4  -405 

586  3 

25 

444  -05 

10 

13 

03 '44 

+0-76 

04  -20 

0-63 

4-503 

290  7 

31 

863  -29 

153 

07 

06-91 

+0-60 

07-51 

0-63 

4-909 

644  5 

81 

216-55 

16 

39 

50  -58 

—0  -40 

50-18 

0-63 

4-711 

876  7 

51 

508  -24 

12 

52 

36  -62 

+1  -05 

37-67 

0  -96 

4  -386 

965  4 

24 

376-17 

35 

04 

08  -49 

-fi  -08 

09  -56 

0  -96 

4  -798 

27S  I 

62 

846  -08 

132 

03 

1376 

_  +1  -90 

15-66 

0-97 

4-909 

644  2 

81 

216  -49 

23 

05 

40  -06 

+1-82 

41  -88 

I  -08 

4-405 

586  5 

25 

444  -06 

104 

20 

18-89 

+0-82 

19-71 

1  -07 

4  -798 

278  2 

62 

846  -09 

52 

34 

00  -94 

+0-70 

01  -64 

f  -08 

4-711 

876  7 

51 

508  -24 

16 

29 

02-56 

+0-13 

02  -69 

I  -93 

4-503 

290  0 

31 

S63  -24 

117 

37 

44-52 

+0  -01 

44  -53 

I  -93 

4-997 

790  0 

99  492  '42 

45 

53 

17  -70 

+0  -87 

18  -57 

1  -93 

4  -906  481  9 

80 

627  -26 

IS 

22 

2475 

+0-41 

25  -16 

I  -62 

4-405 

586  I 

25 

444  -04 

6.S 

50 

56-50 

+0-24 

56-74 

I  -62 

4-876 

702  I 

75 

283  -90 

92 

46 

43  '05 

—0  -09 

42-96 

I  -62 

4  -906  481   9 

80  627  -26 

] 

53 

22  -20 

+  0  -29 

22-49 

0  -21 

4  -386  965  3 

24 

376-16 

5 

50 

41  '36 

—0-19 

41  -17 

0  -21 

4  -876 

702  I 

75 

283  -90 

172 

15 

55  -87 

-^-I  "lO 

56  -97 

0  -21 

4-997 

789  9 

99 

492  -40 

37 

42 

07-37 

-fo-05 

07-42 

2  -04 

4-711 

876  7 

51 

508  -24 

106 

48 

35-10 

+0-63 

35  -73 

2-05 

4  -906  481  9 

80  627  -26 

35 

29 

22-39 

+0-59 

22  -98 

2-04 

4  -689  285  I 

48  897  -33 

54 

1 1 

09-93 

4-0-17 

10  -10 

3-34 

4-909 

644  I 

81 

216-47 

96 

35 

31-66 

-0-13 

31  -53 

3-35 

4-997 

789  9 

99  492  -40 

29 

13 

27-13 

+1  -27 

28  -40 

3-34 

4-689 

285  I 

48  897  -33 

Resultmg  auf^les  i 


27 


28 


29 


31 


32 


33 


34 


Blood 
labim 
Currahee 

Skitt 

Rabun 

Currahee 

Blood 
Rabun 

Skitt 

Skitt 

Blood 

Currahee 

Sawnee 

Blood 

Currahee 

Sawnee 

Skitt 

Currahee 

Sawnee 

Blood 

Skitt 

Grassy 
Blood 

Skitt 

Grassy 

Skitt 

Sawnee 

Grassy 

Blood 

Sawnee 


PHE 

,    M 

AIN    T] 

<IANGU 

LATIC 

)N. 

175 

he  third 

or  South  Carolina 

section 

of  the  It 

■ianf;iilation — continued. 

observed 
angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

i-og. 
'iistances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

56 

04 

32-13 

+  0-46 

32  -59 

2-59 

4-798 

277  9 

62 

846  -04 

83 

42 

55  -f^ 

I  -19 

53  ■■"'5 

2-59 

4  -876 

702  0 

75 

283  -88 

40 

12 

42  '11 

-0-79 

41  -32 

2-58 

4-689 

285  I 

48  897  -33 

47 

41 

35  -68 

to  -02 

35  -70 

2-25 

4-689 

285   1 

48  897  -33 

5X 

42 

51  -16 

Q-OO 

51  -16 

2-25 

4-752 

074  5 

56 

503  -38 

73 

35 

40  -63 

-0-75 

39-88 

2  -24 

4-802 

267  7 

63  426  06 

48 

09 

29-51 

-f  0  "62 

30-13 

]  -29 

4  -689 

285   1 

48  897  -53 

29 

04 

48  -28 

-1  I  -38 

49  -66 

I  -29 

4-503 

801  0 

31 

900-76 

102 

45 

43  74 

+  0-34 

44  -08 

I  -29 

4-806 

272  9 

64 

013  69 

76 

10 

57 '23 

-0-18 

57-05 

I  -70 

4-806 

272  8 

64 

013  -68 

29 

38 

02  -87 

-1-38 

01  -49 

I  -70 

4-513 

146  5 

32 

594  -66 

74 

II 

06  -57 

— Q-OI 

06  -56 

I  -70 

4  -802 

267  6 

63 

426  -04 

122 

20 

36  'oS 

+0-61 

36-69 

0-75 

4-752 

074  5 

56 

503  -39 

28 

29 

21  -55 

—  0-21 

21  -34 

0-74 

4  -50.1 

801   I 

31 

900-76 

29 

10 

03-11 

+  1  -09 

04  -20 

0-74 

4-513 

146  5 

32 

594 -66 

45 

25 

06-66 

-I  -26 

05-40 

2-84 

4-752 

074  4 

56  503  -38 

86 

01 

20  -96 

+0-58 

21  -54 

2-84 

4  -898 

401  0 

79 

140  -91 

48 

33 

40  '37 

+  1-21 

41  -58 

2-84 

4  774 

311  9 

59  471  -92 

12 

II 

II  -86 

-0-34 

u  -52 

0-71 

4-503 

Soo  9 

31 

900-75 

14S 

25 

1376 

-0-52 

13-24 

0-71 

4  -898 

401  0 

79 

140-91 

19 

23 

37 '25 

^0-I2 

37-37 

0-71 

4-700 

5389 

50 

180-95 

33 

13 

54 -Si 

—0-92 

53-89 

I  -39 

4-513 

146  5 

32 

594  -66 

57 

31 

59  "41 

+0-78 

60  -19 

1-38 

4-700 

539  0 

50 

180-96 

89 

14 

10  -16 

—0-08 

10  -08 

1-39 

4  774 

311  9 

59 

471  -92 

35 

35 

42-56 

+  2  -87 

45-43 

I  -26 

4-513 

146  5 

32 

594  -66 

89 

29 

53-97 

+  0-88 

54  -85 

1-27 

4-748 

161  8 

55 

996  62 

54 

54 

23-31 

+0  -21 

23-52 

I  -27 

4-661 

044  I 

45 

81S-S4 

62 

46 

49-64 

-1-63 

48  -ol 

I  '34 

4-700 

538  9 

50 

180-95 

34 

19 

46 -86 

-0   30 

46-56 

1  -34 

4-502 

751  8 

31 

823  -78 

82 

53 

29-47 

— Q-OI 

29-46 

I  -35 

4-74S 

161  8 

55 

996 -62 

98 

22 

32  20 

+  1  -24 

33  -44 

I  -23 

4-774 

311  9 

59 

471  -92 

31 

57 

54  -56 

-l-Q-IO 

54  -66 

I  -22 

4  -502 

751  8 

31 

S23  -78 

49 

39 

34-66 

+0-91 

35-57 

I  -22 

4-661 

044  3 

45 

818 -86 

176 


THE    EASTERN    OBLIQUE    ARC. 

Adjustment  of  the  position  of  Dlount  Alitc/iell  in  North  Carolina,  jSjO-iSg^. 

No.  27. 


Roan  High  BlsmfiF 


Wo/forci 
Kilometers 


Poore 


0  30  «)  50 

Statute  Miles 


Roan  High  Bluff,  A.  H.  B.,  1S94. 
'^^^^.  Ohiects  observed. 


Directions  from  pre- 
vious adjustments. 


Correc- 
tions. 


Final 
seconds. 


Poore 

Benii 

Mount  Mitchell 

Rogers 
Poore,  C.  O.  B.,  1S77;  A.  H.  B.,  1S95. 

King 

Benn 

Mount  Mitchell 

Roan 

Rogers 
Benn,  C.  O.  B.,  1S77;  A.  H.  B.,  1S95. 

King 

Wofford 

Hogback 

Mount  Mitchell 

Roan 

Poore 


o  00  00  'oo 

50  00  44  '04 

103  30  25  -24 

307  22  59  -43 

o  00  00  "OO 

31  55  20-57 

64  iS  17  •14 

84  56  1376 

144  19  49  'So 

O  00  00  '00 

59  06  35  -87 

91  23  08  '81 

150  50  13  '90 

iSi  58  00-63 

258  56  36-11 


4  "94 


0-37 


+5 


55 


20-30 


'7 '51 


19-44 


THE   MAIN   TRI ANGULATION. 

Adjustwcul  of  the  position/ of  Mount  Mitclull  in  Nortli  Carolina,  i8j6-iH()^ — conlinued. 
King,  C.  O.  B.,  i'f^ie--]-]. 


177 


Number  of 
directions. 


Objects  observed. 


Directions  from  jire- 
vious  adjustments. 


Wofford  O 

Hogback  23 

Mount  Mitchell  61 

Benn  77 

Poore  1 24 
Wofford,  C.  O.  B.,  1876. 

King  o 

Hogback  242 

Mount  Mitchell  277 

Benn  316 

Hogback,  C.  O.  B.,  1S76. 

Benn  o 

King  34 

Wofford  73 

6  Mount  TMitchell  309 

N.  B.— Observations  from  Paris  in  1S75  were  too  rough  for  use. 

Conditional  equations. 

1.  0=4-     4-3— 0-92(1)+  3-98(2)-   1-86(3) 

2.  o=-i42-o-5  ■87(2)  +  ii  -35 (3)  — 16-28(4) 

3.  0=+  70 -0-5 -02(3)  +  ! I -69(4)-  3-17(5) 

4.  0=+     1-1-4-03(4)+  8-47(5)-^  4-17(6) 
Correlates. 

I      C,  C,  C,         C4 


00 
20 

35 
18 

'9 

00 
02 
39 

24 

00 

39 
21 

37 


00  -00 
26  -87 
36  -94 
24  -23 
48  -64 

00  -00 

40  -84 
32  -86 
52-16 


03-12 
22  -76 
16  -84 


— o  -92 

+3  -98- 
-1-86- 


4192 — No.  7- 


-  5 -87 

-II  '35-  5  "02 
-16  -28+11  -69-4  -03 
-  3-17+8-47 
-4-17 
Normal  equations. 

0=+     4 -3+20 -146  C—  44 '474  C=+     9 '337^3 
o=— 142-0  4-428-31802-247-29003—  65 -60S  C4 

0=+  70-0  •  171  -905  C3—  73  -961  C4 

0=+     I  -I  +105-371  C4 

C.  =  -r5  "3648 

C,=  +3-5738 

C3=-r4-9S63 

C4= +  1-2643 
// 

(n  =  -4-94 

(2)  =  +o-37 

(3)=-^5'55 

(4)  =-4 '99 

(5^  =  -5-io 

l6)  =  -5-27 


Correc 
tions 


4-99 


5-10 


Final 
seconds. 


31  95 


27-76 


-5-27 


II  57 


■12 


178 


THE    EASTERN    OBLIQUE    ARC. 


Tifnit/liiKj  avijley:  (ind  siden  from  (he  adjiistiiu'iit  uiade  la  (lilcriiihif  the  poxiticm  of  Movnt  Mitchell 
No.  stations.  Observed  angles 


Correc- 
tion. 


Spher- 
ical 
ansfles. 


Spher- 
ical 
excess. 


Log.  dis- 
tances. 


Distances 
in  meters. 


I  Mount  Mitchell 

1  I  Roan 
[Benn 

f  Mount  Mitchell 

2  I  Poore 
[Benn 

I  Mount  Mitchell 
Poore 
King 

[Mount  Mitchell 

4  King 
[wofford 

f  Mount  Mitchell 

5  I  Wofford 


I  Hot 


back 


95 

53 

22 

48  -23 
36  26 

1-89 
I  -89 

4  '864  260 

I 

7i 

159-22 
064  -29 

29 

41 

20 

-4-94 

4-77; 

325 

0 

59 

31 

07 

46 

•73 

-5-55 

41  -is 

1-89 

4-579 

630 

9 

37 

986  -64 

39 
32 

30 
22 

56-41 
56-94 

3-33 
3 '34 

4-846 

167 

T 

70 

172  -S2 

56 

•57 

+0  "37 

4-771 

325 

1 

59 

064  -30 

loS 

06 

22 

•2! 

—5 '55 

16-66 

3  -33 

5  -020 

471 

2 

104 

S26  -53 

52 
64 

57 
18 

4S  -39 
17-51 

7-53 
7-53 

4  -973 

5  -026 

743 
3S8 

9 
2 

94 
106 

133  -44 

264  -5" 

17 

•14 

+0  -37 

62 

44 

1 1 

•70 

+4-99 

16  -69 

7-53 

5-020 

471 

2 

104 

S26  -53 

34 
61 

04 
35 

ID  -811 

S  'OCi 

4  -800 

210 

3 

7 

63 
94 

126  -29 
308  -69 

36 

•94 

-4-99 

31-95 

5  -o-' 

4-974 

551 

82 

20 

27 

•14 

+5'io 

32  -24 

4-99 

5  -026 

388 

3 

106 

264  -52 

20 

39 
36 

07  '47 

I  -86 

4  '602 

019 

781 

6 

39 
66 

996  -28 
036  -08 

35 

52 

•02 

—5  'lo 

46-92 

I  -86 

4-819 

3 

123 

44 

05 

•92 

+5 '27 

1 1  -19 

I  -86 

4-974 

551 

7 

94 

308  -69 

7.    FIRST   SECTION   OF    THE    TRI ANGULATION    WEST    OF 
GEORGIA    AND    ALABAMA,    I<S73- 


THE    ATLANT.\    BASE    NET, 

1 875- 


Gulf  Point  r> 

\^^ 

Johjxa 

"t             Grassy;^ 

(^Brandon. 

/Lavender 

V\GEORGLA^ 

i^ 

^^^^^iPine  Log 

ALABAMAX        // 

\   Sweat  Mt. 

Indian. 

' — 

^^^^Q^^ 

Carnes 

Kencsa-w 

Kilometers 

10       0         10 

20 

30           40           50          60 

Statute  Miles 

70 

80        90      100 

10              0 

10 

20               30 

40 

60                     60 

This  triangulation  is  located  in  Georgia  and  Alabama,  and  is  of  the  same  complex 
character  as  the  Atlanta  ba.se  net.  It  depends  for  the  length  of  its  sides  upon  the 
Atlanta  base,  and  on  the  accompanying  sketch  is  shown,  by  two  heavy  lines,  the 
connection  with  the  base  net.*     The  section  depends  for  the  length  of  its  sides  directly 


*'rhe  computation  and  adjustment  made  in  187,5  and  retained  here  has  no  corrections  applied  to  the  directions  for 
height  of  stations  observed.  These  are  too  small  in  comparison  with  the  observing  error  to  require  special  consideration- 
In  a  newcomp\itation  it  would  have  sufficed  to  limit  the  iecoiuh  of  the  angular  directions  to  two  places  of  decimals. 


THK    MAIN    TRIANGULATIOX. 


179 


■46.      From  the  approximate  probable  errors  of  the  observed 


upon  the  Atlanta  base.  It  is  composed  of  22  triangles.  The  angles  were  measured 
by  Assistants  F.  P.  Webl)er  and  C.  O.  Boutelle,  in  the  j-ears  1^73-74-75,  and  five 
different  in.struments  were  employed.  Weights  to  the  .several  directions  were  intro- 
duced in  the  adjustment,  depending  in  part  on  the  approximate  probable  errors  of 
the  observations  at  a  station  and  in  part  on  the  closing  errors  of  the  triangles.  We 
have  the  mean  error  of  a  triangle  from  the  sum  of  the  squares  of  the  closing  errors 

—  -x-?-^ —  =iti"'69,  and  that  of  an  angle  =±o"'y7;   also  the  probable  error  of  a  direc- 

V       22 

I  '69 
tion  =^  o"674  —^  =  ±0 

directions,  as  given  in  the  aljstracts  of  the  respective  .stations,  we  have  the  average 
value  f,  =  ±o"'i8,    hence  the    .square  of  the  triangle  combination  error  fj=  (o'46/ 

—  (o'lS)-  =  o'i8,  and  adding  this  to  the  square  of  f,,  we  have  t^—  i  p  —  e^^+e^,  whence 
the  relative  weight  p  to  each  direction.  We  have  also  the  ratio  of  the  greatest  to  the 
least  weight  2  "53  to  i. 

The  approximate  heights  of  the  stations  above  the  Atlantic  are  as  follows: 

Meters.         Feet. 

Carnes  396  9  i  302 

Lavender  5i5'2  i  690 

Johns  577 •-!  I  S94 

Indian  603-4  I  9S0 

Gulf  673-3  2  :>09 

Brandon  SH'S  i  679 


Abstracts  of  horizontal  directions  at  stations  coinposiiig  tlic  first  section  2eest  of  the  ^Itlanta  base  net. 


Kenesa-iC,  Cobb  County,  Georgia.     June  23  to  July  iS,  1S73.     75""  direction  theodolite  No.  i.     F.  P. 

W'ebber,  observer. 

Correclioii.s 
Kesmiiii^  uiiceiKiiis 

objects  observed. 


Nuniherof 
directions. 


Resulting  directions     f^^   ^^^j„  t-  Final 

from  previous  ad-        ,„e„t  of  first  seconds. 

justuient  of  net. 


nient  ot  first 
i«ction. 


Sweat  Mountain 
Carnes 
Lavender 
Pine  Log 


o  00  00  -049 

224  20  15-063 

252  07  00  -702 

303  37  22-129 


-2  019 
2  -009 


13  "044 
02  -711 


Pine  Log,  Bartow  County,  Georgia.     July  29  to  September  17,  1S74.     30^'"  repeating  tlieodolite  No.  32. 

F.  P.  Webber,  ob.server.        ; 


2 

Carnes 

3 

Indian 

Coosa 

4 

Lavender 

5 

Gulf  Point 

6 

Johns 

Cohutta 

Gra.ssy 

Sweat  Mountain 

Kenesaw 

0 

00 

oo-ooo 

— 0 

•710 

59 

■290 

22 

30 

3^  '597 

-t-i 

•030 

39 

•627 

",6 

1 7 

34  '507 

46 

2S 

-f  0 

•225 

•35 

'753 

7« 

>9 

50  -280 

-i  0 

•251 

50 

■531 

84 

39 

43  •143 

-^  0 

■471 

43 

-614 

141 
193 

2S5 
■;o8 

29 
10 

12-849 
39  "409 
1  •  339 
39-128 

correction 

19 
;eau 

^ 

-  0 

253 

I  So 


THE   EASTERN   OBLIQUE   ARC. 


Abstracts  of  horizontal  directions  at  stations  composing  the  first  section  west  of  the  Atlanta  base  net, 

/S^j-iSy^ — continued. 


Sweat  Mountain,  Cobb  County,  Georgia. 

No.  I. 


Number  of 
directions. 


Objects  observed. 


September  lo  to  October  3,  1873. 
F.  P.  Webber,  observer. 

Resulting  directions 
from  previous  ad- 
justment of  net. 


75^™  direction  theodolite 


Corrections 
from  adjust- 
ment of  first 
section. 


Final 
seconds. 


Kene.saw 
Carnes 
Pine  Log 
Grassy 


o 

32 

100 

145 


00  00 '016 

34  43  '017 

54  55  "552 

16  24  -564 


-o  '203 


42  -814 


Grassy,  Pickens  County,   Georgia.     July   13  to    28,   1874.      ^o""  direction   theodolite   No.  3.     C.  O. 

Boutelle,  observer. 


0 

00 

GO  '228 

43 

29 

35  '930 

51 

39 

31  -927 

86 

41 

37  784 

131 

59 

17  -061 

183 

15 

38  -93 

261 

37 

28  -06 

297 

13 

10-62 

Sawnee 

Sweat  Mountain 

Kene.saw 

Pine  Log 

Johns 

Cohutta 

Blood 

Skitt 

Carnes,  Polk    County,  Georgia.     November  17   to   December   27,    1873 

No.  32.     F.  P.  Webber,  observer. 

^  J  Results  from  local 

'   ■  adjustment. 


O  00  00  '000 

7  04  48-139 

183  44  53 '383 

230  04  00  -691 

232  44  12-747 

310  57  24-950 

317  59  30-451 

348  14  27  -327 


-2-193 


14  -868 


30""   repeating   theodolite 


Number  of 
directions. 

Objects  ol 

14 

Kenesaw 

Lost  Mountain 

10 

Indian 

Coosa 

II 

Lavender 

12 

Pine  Log 

Pine  Mountain 

13 

Sweat  Mountain 

jproximat 

probable 

error. 

;        Corrections 
from  adjustment 
of  first  section. 

// 

// 

ito-io 

-0  -456 

0-14 

0-I2 

-I  '345 

o-i6 

0-I2 

-|-o  -920 

o-jo 

-0  -045 

0-14 

0  -12 

+0  -934 

Final 
seconds. 


59  '544 
52  -038 


13  -667 
24-905 

28  -261 


Mean  correction  — o  -002 


THE   MAIN   TRIANGULATION. 


l8l 


Abstracts  of  horizontal  directions  at  stations  composing  the  first  section  7vest  of  the  Attanta  base  net, 

1873-1875 — continued. 

Lavituder,  Floyd  County,  Georgia.     October  12,  1874,  to  January  30,  1875,  and  August  6  to  12,  1875. 
jQriii  repeating  theodolite  No.  32.     F.  V.  Webber,  ob.server. 


Number  of 
directions. 

Ol)jects  olwerveil 

19 

Pine  Log 
Pine  Mountain 

20 

Kenesaw 

21 

Carnes 
Coosa,  mark 

15 

Indian 
Weisner 

16 

Brandon 

17 

Gulf  Point 

18 

Johns 
Cohutta 

Results  from  local 
adju.stment. 

o  /  // 

O  GO  00  "GOO 

17  49  59 ''SS 

30  20  51  -197 

55  18  18-473 

63  25  38-315 

III  29  54  716 

137  35  38  -33 

189  35  31  -660 

244  10  24  -069 

297  42  46  -291 

316  04  49  "376 


Approximate        Corrections 
probable       from  adjustment 


error. 
// 
±0  -07 
o-i6 

O'll 
Q-IO 

o  -09 
o  -09 

0-32 

o-o8 
o-oS 

o  "II 

O  '12 


of  first  section. 


H-o  -324 


Final 
seconds. 


Of  J  -324 


—  I  -058 
— o  -267 


+0  '234 


+0-171 
+0  -673 

— o  'loS 


50  139 

18 -206 

54  950 

3'  •«3i 

24-742 
46-183 


Mean  correction   —  o  -004 


/o//;/5.  Walker  County,  Georgia.     May  12  to  June  21,1875.     30™  direction  theodolite  No.  107.     F.  P. 
Webber,  observer.     Circle  used  in   XXI  positions. 


26 

Gulf  Point 

Pigeon 

High  Point 

Cohutta 

22 

Grassy 

23 

Pine  Log 

24 

Indian 

25 

Lavender 

o 

17 

44 
145 
191 


00  00  -ooo 

13  25  -438 

15  12-782 

15  56-8 

23  00-153 

217  34  29-722 

294  07  26  -733 

297  06  13-557 


zbo  "lo 
0-31 
O  '20 


+0-394 


0-20 
0-24 

o-i6 
o  -20 


—  I  -240 
-^o  -672 
-ro  -247 

—  I  -102 


00-394 


58-9'3 
30-394 
26-980 

13  455 


Mean  correction   — o  -006 


Indian,  Cherokee  County,  Alabama.     July  24  to  August  21,  1875.     30™'  direction   theodolite  No.  loS. 
F.  P.  Webber,  observer.     Circle  used  in   XVII  positions. 


29 

Lavender 

30 

Johns 

Cohutta 

Coosa 

31 

Pine  Log 

32 

Kenesaw 

33 

Carnes 

Cheehahaw  * 

Aurora 

27 

Brandon 

28 

Gulf  Point 

0 

00 

00  -QOO 

±0-06 

-0  -244 

59  756 

3 

14 

05  -050 

0-17 

—0-176 

04  -874 

15 

28 

22-9 

16 

44 

04  -052 

0-22 

44 

32 

I  I  -956 

0-15 

^i  -991 

13  "947 

72 

53 

48-127 

0-12 

+0-729 

48  -856 

74 

49 

05  -144 

0-15 

—0  -504 

04-640 

1S9 

16 

07  -563 

259 

21 

48  -653 

0-I2 

301 

16 

21  -883 

o-i6 

-0  397 

21  -4S6 

335 

22 

53  '053 

o"i5 
^Nlean  correction 

-I  -41S 

51  -635 

—0  -i.x-1^ 

*  Observed  December  3  to  19,  1885,  by  O.  H.  Tittmatm,  with  sot™  directiou  theodolite  No.  114. 


l82 


THE    EASTERN    OBLIQUE    ARC. 


Absiiacts  of  horizonlal  directions  at  stations  ioniposiug  the  first  section  zvcst  of  the  Attanta  txise  net, 

jS/j-/S/j — continued. 

Gut/' Point,  WaWcer  County,  Georgia.     Septemlier  14  toOctoberg,  1S75.     30'"'  ilirection  theodolite  No. 
108.     F.  P.   Webber,    F.  D.  Granger,  and    J.  H.  Christian,  observers.     Circle  used  in  XVII  positions. 


Number  of 
directions. 

Obje 

High  Point 

Pigeon 

Cohutta 

34 

Johns 

35 

Pine  Log 

36 

Lavender 

37 

Indian 

38 

Brandon 

Gunter 

Objects  obser\'ed. 


Results  from  local 
adjustment. 


O  GO  GO  'GOO 

28  39  II  -071 

55  29  34-156 

75  49  36  751 

99  04  14-149 

139  23  30-004 

162  05  54  '020 

210  oS  59-511 

250  G4  42  -408 


Approximate        Corrections 
probable        from  adjustment 
error.  of  first  section. 


±0-08 
0-32 

o  -16 

0-25 
0-18 

G  -14 
G  -20 
G  -17 
0-45    . 

Mean  correction 


Final 
seconds. 


—  I 

•391 

+0 

•959 

—  G 

•138 

+  0 

-362 

+  0 

■054 

35 '360 
15-1G8 
29  -866 
54  '382 
59  '565 


±0  -II 

0  -19 

G-36 

-0  -338 

13-818 

0-30 

+  0-138 

54-576 

0-31 

+0  -164 

43  "165 

0  -21 

Brandon,  Dekalb  County,  Alabama.     December  6  to  26,    1S75.     30"^"'    direction    theodolite   No.  ig8. 

F.  P.  Webber,  observer. 

o  /  //  //  //  // 

Aurora  o  00  00  -qog 

Gunter  61  36  36  -507 

39  Gulf  Point  16S  10  14-156 

40  Lavender  222  49  54  -438 

41  Indian  266  og  43  -goi 
Weisner  293  13  43-092 

Mean  correction   — o-oii 

Observation  equations. 
I       0=^0-472-    (l)+    (2)-(l2)  +  (l3) 
II      o=-o-426-    (7)+    (i)-(i3)r(i4) 

III  G=+3-i67-   (8)+   (4)-(i9)-f(2G) 

IV  G=-3-443-(ii)  +  (i4)-   (7)+   (8)-(2G)+(2i) 
V    ■o=+o-752-   (6)4-   (9)-(22)  +  (23) 

VI     o=+o-G95-(i8)+(i9)~    (4)+   (6)-(23)-l  (25) 

VII     0= -0-544- (10) +  (12)-    (2)+   (3)-(3i)  +  (33) 

VIII     o=-2-505-(io)  +  (ii)-(2i)+(i5)-(29)4  (33) 

IX     o=--2-293~   (5)+   (6)-(23)  +  (26)-(34)  +  (35) 

X  I  o=-2-o34-(28)  +  (3i)-   (3)+   (5)-(35)^  (37) 

XI     G=-3-i44~(28)  +  (3o)-(24)  +  (26)-(34)4(37) 

XII     o=-o-i2o-(27)  +  (29)-(i5)-!-(i6)-(4G)  +  (4i) 

XIII  G=-^i-i67-(i6)f(i7)-(36)  +  {38)-(39)+(4o) 

XIV  o=+o-827-{27)  +  (2S)-(37)  +  (38)-(39)-|  (41) 
XV      0=  +  I -382+0-8286  ( 14 )  — I -Gi  14  (13)4-0- 1828(  12)— 0.3295(1) +0-1664  (2) 

XVI     o=+8-o23+6-6oi4(  14) -6-6014(10) -0-0398  (7)  +  i2-5i7i(33)-i2-8777(32)+G-36o6(3i) 
-o-6745(2)+o-5o8i(3) 


THE    MAIN    TRIANGULATION. 


1^3 


XVII 


XVIII 


XIX 


XX 


XXI 


XXII 


XXIII 


o=  I  8-667  |-6-6oi4(  14)— 6-6014(10) —(V59_^4{2i)  i  0-4524(20)  -  ()-i4io(  r.S) —12-8777 (32) 

+0-3997(8) -o-3997( 7 )  I  1 2 -8206 (33 )  +0-057 ' ( 29) 
0= -t- 1-425  -0-2868(21)  f  0-1410(15) -I  o.  1458(19) +0-3035(33) -fo-o57i( 29) -0-3606(31) 

+0-3081  (2) H  o-2()tx)(4)  -0-5081(3) 
o=-o-7or-4-oo6i(25)-|-4'045o(24)-o-o389(23) -3-51 15(29)  .3-7255(30) -0-2140(31) 

-I  0-7414(4)^0-2677 (6) -0-4737(3) 
o=  — 1-290-4-1528(25)  14-0450(24)  10-1078(26)     4'i<'^5'>(29)  — 3725S(3o)^o-4595(28) 

-0-6079(36)40-1047(34)  ^  0-5032(37) 
o=— 0-736+0-2662(18) -0-1556(1 7)— 0-1 106(19 1-0-1047(36) —0-3855  (34) -0-4902(35) 

-0-2677  (4)  -0-5564(6)  1  0-8241  (5 ) 
o=+o-2i9-o-33i6(29) -I  0-4595(28) -01 279(27) -0-4297(36) +0-5032  (37) -0-0735(38) 

+o'3737(4o) -0.2244(40-0-1493(39) 
o=  — 1-514-0-1106(18)— 0-3596(20) +0-4702(19) -<>-<j3S9( 25)— 0-4281  (22) +0-4670(23) 

—0-1674(8) —0-2084(9) 


The  reciprocals  of  the  relative  weights  to  the  several  directions  introduced  into  the 
correlate  equations  are  as  follows: 


direc- 
tion. 

I 
P 

Direc- 
tion. 

1 

7 

Direc- 
tion. 

1 

7 

Direc- 
tion. 

I 

7 

r 

1  ■13 

12 

0  -87 

23 

I  -08 

34 

I  -11 

2 

0  -88 

13 

0  -90 

24 

0  -95 

35 

097 

3 

0  -90 

14 

0-S7 

25 

1  -OI 

36 

0  -92 

4 

0  -86 

15 

0-87 

26 

0  -88 

37 

I  01 

5 

1 1  'Sg 

16 

0  -86 

27 

0-94 

3« 

()  -96 

6 

0  -90 

'7 

0-S6 

28 

0-93 

39 

I  -40 

7 

1  '43 

18 

0-89 

29 

0  -85 

40 

I  -24 

8 

2-15 

19 

0-85 

30 

0  96 

41 

I  -26 

9 

I  -14 

20 

0-S8 

31 

0-93 

10 

0  -90 

21 

0-87 

32 

0  -89 

1 1 

0  '89 

22 

1  -oi 

33 

o'93 

The  average  value  of  —  eijuals  1. 
P 


C4 


No. 

I 

o=— 0-472 

2 

-0-426 

3 

+3-167 

4 

-3 '443 

.S 

+  0-752 

6 

+  0  -095 

7 

0-544 

S 

-2-505 

9 

-  2  -293 

10 

-2-034 

II 

-3' 144 

12 

—  0120 

13 

-1-167 

14 

+  0-S27 

15 

+  1  -382 

Norma/  cqiiaiioiis. 

C5  C6  C7  Cs 


C9 


C; 


+  3-78       -2 -03 

+  4  -33 


+4-74 


+  2-30 
-3-03 
+  7-09 


+  4  -13 


Ci, 


Cm 


gS 

—  I  -gS 



59 

+  5-41 

+ 1  -gS 
+ 1  -S3 
+5-31 

+5  -^3 

-1-^3 

-I-S6 

+5-63 

+  1  99 
+  1-94 

+5-S4 

-I  -72 
+6 -02 

-3-10 

+6-24 

-1-94 
-1-94 

-h2-30 

+  2-56 
+6-50 

1 84 


THE    EASTERN    OBUOUE    ARC. 


Normal 

equations 

— completed. 

No. 

C15 

CIS 

C17 

C.3 

CD 

C20 

C=i 

C2= 

c=? 

I 

-0  -55054 

-0  -59356 

+  0-27113 

2 

+  1-25881 

+5  -S0013 

+6-31479 

3 

-0-46125 

+0  -04807 

+0  -63760 

+0-13621 

—0-35621 

4 

+0  -72088 

+5  -S0013 

+6-25978 

-0-21952 

-0  -04346 

5 
6 

+0-19892 
-4  -88268 

+0  -50076 
—0  -60147 

+0-69916 
-0  -04555 

—0  -04807 

-4-19433 

7 

+  0  '01261 

+  lS -29765 

+  17-86441 

— 0-noSi 

-0-22731 

8 

+17-58216 

+18-45481 

+0  -60590 

+  2-98477 

+  3-55724 

+0.  28 1 86 

9 

-0-19892 

—  0-02136 

—0  -330S2 

—0  -50436 

-0-12193 

+0 -12193 

+0-22731 

+0  -0S090 
—0-20673 

+  0-25796 
+  0-42790 

+0  -0S090 
+0  -08090 

II 

—0-26627 

12 

-0-07413 

-0-07413 

-2-98477 

-3-55724 

—0  -90776 

13 

+0  -55927 

—0  -03750 

+0-99717 

14 

—0  -0S090 

—0-10495 

15 
i6 

+ I -69408 

+4  -66006 
+371  -19343 

+4  -75SS3 
+373  -99329 

+0-04512 
+  2-99686 

o=+S 

•023 

-0-28839 

17 

+8  -667 

+378-66768 

+3-78681 

-0-17042 

—0-2031 1 

—0  '01609 

—0-28702 

1 8 

+  ■ 

■425 

+0-66659 

+0-24549 

—  0-203 1 1 

-0  -05975 

-0-01609 

+0-05S27 

19 

— o 

701 

+  56-34184 

+58-16226 

—0  -03663 

+  0-98975 

+  0-13778 

■290 

7.^6 

+61 -987S4 

+0-01375 
+  1-44710 

+ 1  -S7200 

21 

—  0 

+0-04139 

—  0  "07041 

22 

+  0 

■219 

+  1-00383 

23 

—  I 

■514 

+0  -84453 

C,  =  -o-323i 
C,=  -o-7i34 
C3=+o-4736 
C4=^-i  -1388 
C5  =  "0-89i7 

C6  =  — O  -16SS 


Resulting  correlates. 


C  7  =  -0-2582 
C  8  =  +  2  -1722 
C  5= +0-8873 
Ck.= +0-3726 
C„  =  -o-2i98 
C,;  =  -i-i  -1322 


C,3=  + 0-9330 
C,4  =  — 0-8156 

C,5= -0-6398 
Ci6  =  — 2  -S112S 

C,7  =  +  2-7477 
C,s=-8-2i62 


C,,=  +  2  -0506 
0=0=- 2  -0409 
€=,  =  +0-9664 
0^2= +0-8278 
C.,  =  -f-4"95ii 


Resulting  corrections  to  otiiicrved  directions. 


(  I)= 

=  —0-2028 

(     2) 

—0  -7101 

(  3) 

+ 1  -0297 

(   4) 

+0-2247 

(   5) 

+0-2512 

{   6) 

+0  -4706 

(  7) 

—  2  -01S9 

(   8) 

+  2  -0094 

(  9) 

-2-1929 

(10) 

-I  -3448 

(11) 

+0-9197 

(12)  = 

=  -0-0452 

(13) 

^0  -9336 

(14) 

-0  -4563 

(15) 

+0  -2338 

{16) 

+0-1713 

(17) 

+0  -6730 

(IS) 

—0  -loSo 

(19) 

+0-3237 

(20) 

-1-0584 

(21) 

—0-2671 

(22) 

-I  -2404 

(23)  = 

=  +0  -6722 

(24) 

^0  -2466 

(25) 

—0  -ro22 

(26) 

^0-3937 

(27) 

-0  -3973 

(28) 

-I  +185 

(29) 

-0-2438 

(30) 

-0-1759 

(31) 

+  1  '9913 

(32) 

+0-7289 

(33) 

-0  -5042 

(34)  =  -i  -3909 


(35) 

+0  -9589 

(36) 

-0-1375 

(37) 

+0-3621 

(38) 

+  0-0541 

(39) 

-0  -3380 

(40) 

+0-1375 

(41) 

+0-1643 

:I"-I5. 


Mean  error  of  a  direction  of  unit   weiglit     /  VP'^''^'\  —    /30  i 

y       n  y     2^ 

The  average  weight  being  unity,  we  have  the  probable  error  of  an  observed  direc- 
tion =  ±  o"'79. 


No. 


THK    MAIN    TRIANGULATIOX. 
A'csii/Zinff  arifflcs  and  s/'d/'s  of  the  first  section  west  of  the  Atlanta  lyase  net. 


Oljscrveil  ruiKlfS. 


Correc- 
tions. 


Sj)her- 
ical 


Spher 
ical*' 


angles,     excess. 


l/y^.  dis- 
tances. 


185 


Distances  in 
meters. 


t 


Carnes 
Pine  Log 
Kenesaw 

Carnes 
Pine  Log 
Sweat  Mountain 

Carnes 

Sweat  Mountain 

Kenesaw 

Lavender 
Pine  Log 
Kenesaw 

Lavender 
Kenesaw 
Carnes 

Lavender 
Pine  Log 
Carnes 

Johns 
Grassy 
Pine  Log 

Lavender 
Johns 
Pine  Log 

Indian 
Lavender 
Pine  Log 

Indian 
Johns 
Pine  Log 

Lavender 

Jolms 

Indian 

Indian 
Pine  Log 
Carnes 


49  "2 

51  40 

79  17 

37  '7 

74  22 
6.S  20 

11  45 

32  34 

135  39 

30  20 

98  oS 

51  30 

24  57 

27  46 

127  15 

55  iS 

46  28 

75  13 

26  I  r 

45  17 

loS  30 

62  17 

79  3r 

38  II 

44  32 

III  29 

23  57 

41  18 

76  32 
62  09 

173  47 

2  5« 

3  14 

30  16 

22  30 

127  12 


35  '050 

20  '872 
07  '066 

02  -377 
48  -661 
1 2  -535 

32  -673 
43-001 

44  •9S6 

51  '197 
56  -380 

21  -427 

27  -276 

45  639 
47  '253 

iS  '473 
35  '508 

12  -203 

29  569 
39  '277 
56  -266 

13  709 
43  -835 

07  '635 
1 1  -956 
54716 
56-911 

06  -906 

57-011 

04  '546 

08  -425 

46  -824 

05  -050 

53 -'SS 
3S  "597 
3'  '567 


-o-4ir 
— o  -710 

4-2  -018 

+0  -979 
-o  -710 
+0  -203 

-I  -390 
-0-203 
+  2  -019 

—  I  -382 
+0-225 

—  2  -OK) 
+  0-791 

+4  -028 

-I  -376 

-0-591 

+0  -935 
-o  -965 

^  I  -912 
-2-193 
-0-471* 

+0  -432 

-0773 
-4-0  -246 

+  2-235 
— o  -091 
-o  -S05 

+2-167 

-o  -425 

-0-559 
+0  -342 

-o  -348 
-(-0  -067 

-2-495 
+  1  -740 
-t-i  -299 


34  '639 
20-162 
09  -0S4 

03  '356 
47 '951 
12-738 

3'  '283 
42  -798 
47  '005 

49 'Si 5 
56  -605 
19-4:7 

28  -067 
49  "667 
45  '^77 
17-8S2 

36  -443 
1 1  -23S 

31  +8 1 

37  -084 

55  795 

14-141 
43-062 

07  -88 1 

14-191 
54  -625 

56  -106 


I  -295 
I  -295 
I  -295 

I  -348 
1-349 
1  -348 

o  -362 
0-362 
0-362 

-946 

•945 
■946 

•204 
•204 
-203 

•S54 
•854 
•855 

■453 
•453 
•454 

-695 
-694 

■695 

-641 
■640 
-641 


4-587  666 
4  -604  1 83 
4-701  967 

4-516  084 

4  7 '7  436 
4-701  967 

4  -182  214 
4-604  183 
4717  436 
4-587  666 
4  -S79  77" 
4  -777  750 

4-604  1S3 
4-647  387 
4  -S79  770 

4-701  967 
4  -647  387 

4-777  750 

4  -525  240 
4-732  129 
4  -S57  350 
4-732  129 

4-777  75" 
4-576  176 

4  -777  75" 
4  -900  4  88 

4  -540  524 


09  -073 

3 

-215 

4732 129  0 

56  -586 

3 

-216 

4  -900  488  9 

03  -987 

3 

-215 

4  -859  loS  3 

oS  -767 

0 

-120 

4  -S59  loS  3 

46  -476 

0 

-120 

4  -540  524  3 

05  -117 

0 

•120 

4-576  176  5 

50  -693 

I 

-299 

4-701  967  7 

40  -337 

I 

■299 

4  -582  375  3 

32  -866 

I 

-298 

4  -900  48S  9 

38  696  -03 

40  ! 96  -a8 
50  346-31 

32  815 -,S8 
52  171  -87 
50  346  3' 
15  213 -fX) 
40  196  -08 

52  171  -87 

38  696  03 
75  817-63 
59  944  -70 

40  196  -aS 
44  400  -50 
75  817-63 

50  346-31 
44  400-50 
59  944  -70 

33  5'5-i2 

53  967  -09 
72  003  05 

53  967  -09 
59  9 14  -70 

37  685  69 

59  944  7" 
79  522  29 

34  715-57 

53  967  09 
79  522  -29 
72  295  -01 

72  295-01 

34  715  -57 
37  685  -69 

50  346-31 

35  227  -45 

79  522  -29 


1 86 


THE    EASTERN    OBLIQUE    ARC. 


13 


14 


15 


16 


17 


18 


19 


23 


24 


25 


Rcsnllitig  (!//g/t\ 

and  side 

<i  of  I 

'he  first  se 

eh'on  iL'es/  of  the  Atlanta  ba. 

e  net — conti 

lued. 

stations. 

Obs 

ervec 

angles. 

Correc- 
tions. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

Indian 

74 

49 

05-144 

—0-261 

04  -883 

I  -086 

4  -647  387 

9 

44 

400-50 

Lavender 

56 

ri 

36  -243 

+0  -501 

36  -744 

1-085 

4-582   375 

3 

38 

227  -44 

Carnes 

4S 

59 

19  '364 

+  2  -265 

21  -629 

J  -085 

4  -540  524 

3 

34 

715-57 

Gulf  Point 

23 

14 

37  '398 

+  2  -351 

39  -749 

0-944 

4-732   129 

0 

53 

967  -09 

Johns 

142 

25 

30  -278 

—  0  -278 

30  -000 

0-944 

4-921    107 

I 

83 

388  -67 

Pine  Log 

14 

19 

52  -863 

+0  -220 

53  -083 

0-944 

4-529  538 

0 

33 

848  -38 

Gulf  Point 

40 

19 

15  -855 

—  I  '096 

14-759 

I  •7!3 

4-777   750 

8 

50 

944  -70 

Pine  Log 

23 

51 

14772 

j-o  -026 

14  -798 

I  -7'3 

4-573  619 

2 

37 

464  -44 

Lavender 

.        115 

49 

35  '931 

-0  -349 

35  -582 

I  -713 

4-921    107 

0 

83 

388  -67 

Gulf  Point 

63 

33 

53  '253 

+  1  -254 

54  -507 

0-963 

4-576   176 

5 

37 

685  -69 

Johns 

62 

53 

46  -443 

+0  -496 

46  -939 

0  -962 

4-573  619 

2 

37 

464  -44 

Lavender 

53 

32 

22  '222 

-0-781 

21  -441 

0  -962 

4  -529  537 

9 

33 

848  -38 

Gulf  Point 

63 

01 

39-871 

-0-597 

39  -274 

4-164 

4  -900  488 

9 

79 

522  -29 

Pine  Log 

47 

49 

u  -683 

-0-779 

10  -904 

4-164 

4  -820  337 

1 

66 

1 20  -64 

Indian 

69 

09 

18  -903 

+  3-410 

22-313 

4-163 

4  -921   107 

0 

83  388  -67 

Gulf  Point 

22 

42 

24  'oiS 

+0  -500 

24-516 

0  -810 

4  -540  524  3 

34 

715-57 

Lavender 

132 

40 

29  '353 

+  0  -440 

29  "793 

o-8ii 

4  -820  337 

1 

66 

1 20  -64 

Indian 

24 

37 

06  '947 

f  I   -175 

08-122 

0  -810 

4-573  619 

2 

37 

464  -44 

Gulf  Point 

86 

16 

17  -269 

+  1  -754 

19-023 

J  -893 

4  -859  loS 

3 

72 

295  -or 

Johns 

65 

52 

33  -267 

+0-147 

33  -414 

I  -892 

4  -820  337 

1 

66 

1 20  -64 

Indian 

27 

51 

1 1  "997 

+  1  -243 

13  -240 

I  -892 

4  -529  537 

9 

33 

848  -38 

Brandon 

43 

10 

48  -563 

+0  -027 

48  -590 

I  -248 

4  540  524 

3 

34 

715-57 

Lavender 

78 

05 

36  -944 

—0  -062 

36  -882 

I  -248 

4  -695  837 

9 

49 

640  -70 

Indian 

58 

43 

38-117 

+0-155 

38  -272 

1  -248 

4  -637  099 

2 

43 

360  -99 

Brandon 

54 

39 

40  -282 

+0  -475 

40  -757 

1   -122 

4-573  619 

2 

37 

464  -44 

Gulf  Point 

70 

45 

29  -507 

+0-191 

29  -698 

I      121 

4-637  099 

2 

43 

360  -99 

Lavender 

54 

34 

52  -409 

f  0-501 

52-910 

1   -122 

4-573   '88 

9 

37 

427  -33 

Brandon 

97 

50 

28  -845 

f  0  -502 

29  '347 

'   -559 

4  -820  337 

1 

66 

120-64 

Gulf  Point 

48 

03 

05  -491 

-0-308 

05  -183 

I   -560 

4-695  837 

9 

49 

640  -70 

Indian 

34 

06 

31  -170 

-  1  -02 1 

30-149 

I   -560 

4-573   '88 

9 

37 

427  -33 

Indian 

28 

21 

36-171 

1  -262 

34  -909 

2-509 

4  -587  666 

4 

38  696  -03 

Pine  Log 

74 

10 

59  '469 

]  I  -030 

60  499 

2-509 

4-894  214 

2 

78  38 1  -61 

Kenesaw 

77 

27 



32-118 

2-508 

4  -900  4S8 

9 

79 

522-29 

Indian 

72 

53 

48-127 

1  0-973 

49  -100 

2  -204 

4  -879  770 

2 

75 

817-63 

Lavender 

81 

09 

03-519 

|-i  -292 

04-811 

2  -203 

4-894  214 

2 

78  381  -61 

Kenesaw 

25 

57 

12  -700 

2  -204 

4  -540  524  3 

34 

715-57 

Carnes 

176 

15 

06  -617 

1-0-888 

07  -505 

0  -085 

4-894  214 

2 

78  381  -61 

Indian 

I 

55 

17-017 

-1  -232 

'5-785 

0-085 

4-604  183 

7 

40 

196  08 

Kenesaw 

I 

49 

36  -965 

0-085 

4-582  375 

3 

38 

227  -45 

THE    MAIN    TRIANGULATION. 


187 


8.    THK     SECOND     SECTION    OF     THE    TKIANGULATION    WPZST   OF     THE     ATLANTA     BASE 
NET,    GEORGIA    AND    ALABAMA,    1875^1887. 

This  section  is  of  the  same  complex  composititm  as  the  precedinj:^  section;  it  is 
shown  on  the  following  sketch;  for  distances  and  positions  it  depends  npon  the 
two  sides  marked  by  heavy  lines.  Eight  observers  took  part  in  the  work,  which 
was  executed  between  the  j-ears  1875  and   1887,  but  this  includes  an  interval  of  eight 

No.  29. 


Gu.nter 


Rowe, 


Cheehahaw 
Kilometers 


10  20  30  40  so  60  70  so 

Statute  Miles 


30 


3'ear§  during  which  the  work  was  suspended.  The  figure  comprises  S  new  stations 
connected  by  16  triangles  and  the  adjustment  involves  18  conditions  to  be  .siitisfied. 
From  the  sum  of  the  squares  of  the  closing  errors  of  the  triangles  we  have  the  mean 


error 


V— ^-^  =  ±  i""36  and  that  of  an  angle  dco"'78,  al.so  the  probable  error  of  a 
16 


I  36  , 

direction  =  o'674  —7=  =  ±0  ' 


■37.     Unit  weight  was  assigned  to  each  direction. 


The  approximate  elevations  of  the  .stations  are  as  follows- — 

Mtters.  Heet. 

Gunter  436  1   430  I  Wilson 

Aurora  42S  i  .P4     Wornock 

Rowe  461  I  512     Cahaba 

Sumniit  360  i    iSi      Cheehahaw 


VIeters 

Feet. 

360 

I    iSo 

435 

I  42S 

461 

I   315 

734 

2  407 

1 88 


THE   EASTERN   OBLIQUE   ARC. 


Abstracts  of  horizontal  directions  at  stations  composing  the  second  section  of  the  triangulation  west  of 

the  Atlanta  base  net,  /S/j-fSS/. 

Gutf  Point,  Walker  Count}-,  Georgia.     September  14  to  October  9,  1875.     30""  direction  theodolite 
No.  108.     F.  P.  Webber,  F.  D.  Granger,  and  J.  H.  Christian,  observers. 


Number 
of  direc- 
tions. 


Objects  observed. 


Corrections 
Resulting  directions        from  adjust- 
from  adjustment  ment  of 

of  first  section.  second  sec- 

tion. 


Final 
seconds. 


High  Point 
Pigeon 

Cohutta 
Gunter 


0 

00 

59 

•969 

28 

39 

II 

•040 

55 

29 

34 

•125 

Brandon,   Dekalb  County,  Alabama.      December  6   to  17,   1875 

F.  P.  Webber,  observer. 


59  '969 


250    04    42-377  +0-057  42-434 

30'"'  direction  theodolite  No.   108. 


3 

Aurora 

4 

Gunter 

Gulf  Point 

Indian 

Weisner 

0 

00 

59  -989 

-0  -337 

59  "652 

61 

36 

36  -496 

+0  -93S 

37  -434 

1 68 

10 

13-818 

266 

00 

43  -165 

293 

13 

43  "081 

• 

Indian,  Cherokee  County,  Alabama.  July  24  to  August  18,  1875.  30"^  direction  theodolite  No.  108. 
F.  P.  Webber,  observer.  December  3  to  19,  18S5.  50""  direction  theodolite  No.  1 14.  O.  H. 
Tittmann,  observer. 


Lavender 

Cohutta,  Grassy  Mountain 

Coosa 

Cheehahaw 

Aurora 

Brandon 

Gulf  Point 


o    00  59  -756 

15  28  22  '9 

16  44  04-052 
Sg     16  07  -560 

21  48-650 
16  21  -486 

22  51  -635 


1S9 
259 
301 
335 


— o  -469 
-I  -844 


59  756 


07  -091 
46  -806 


Gunter,  Mar.shall  County,  Alabama.     July  21  to  August  15,  1877.     30""  direction  theodolite  No.  108. 

F.  D.  Granger,  observer. 


18 

Rowe 

14 

Gulf  Point 

15 

Brandon 

16 

Aurora 

17 

Summit 

o  00  00  -oo 

179  48  34  -So 

213  19  17  -So 

276  52  01  -30 

311  07  24-82 

Probable  error  of  a  .single  observation  of  a  direction  {D.  and  R.),  d'l  =  = 
XVII  positions. 


+0-45 
—  I  -12 
+o-6o 
-0-17 

+  0-24 


00-45 

33-68 
18  -40 
01  -13 
25  06 


i'''-5S.     Circle  used  in 


THE    MAIN    TRIANGULATION. 


189 


Abstracts  of  horizontal  directions  at  stations  composing  the  second  section  0/  the  trianf^nlation  west  of 

the  Atlanta  base  net,  /87S-/887 — continued. 

Aurora,  Etowah  County,  Alabama.  June  6  to  20,  1877.  30""  direction  theodolite  No.  108.  F.  P. 
Webber,  observer.  April  14  to  May  8,  1886.  50^^"' direction  theodolite  No.  114.  O.  H.  Tittmann, 
observer. 


Number 
of  direc- 
tions. 


Objects  observed. 


Resulting  directions 
from  adjustment 
of  first  section. 


Corrections 
from  adjust- 
ment of 
second  sec- 
tion. 


Final 
seconds. 


// 

00 'OO 


Azimuth  Mark  o    00    00  -00  .... 

Indian  33     25     53  76  -o  06  53  70 

Weisner  38     53     4330 

7  Cheehahaw  87     46    50-31 

8  Cahaba  148     48     14  -92 

9  Wornock  184     04     18-77 
ID           Summit                                                                           216     19    35  -52 

11  Rowe  257     36     10-13 
Moore  275     36     1 1  -38 

12  Gunter  294     28    55-38  —0-62  54  76 

13  Brandon  349     19     38-19  -ro -68  38-87 
Probable  error  of  a  single  observation  of  a  direction  {D.  and  A*.)  in  1877,  ^,  =  =hi"-So.     Circle 

used  in  XVII  positions. 

Probable  error  of  a  single  observation  of  \  direction  (/?.  and  A". )  in  18S6,  ^,  =  rbo"  -79.     Circle  used 
in  VII  positions. 

Rowe,  Madison  County,  Alabama.    September  3  to  October  9,  1S77.     30'"  direction  theodolite  No.  108. 
F.  D.  Granger  and  J.  H.  Christian,  observers. 


-0-28 

50-03 

^020 

15-12 

-t-0-05 

18-82 

+0-07 

35-59 

—0-05 

10-08 

19 
32 


23           Wilson  o    00    00  -GO            -;-o  -63              00  "63 

Trinity  33     55 

Capshavs?  83     58 

19  Gunter  200 
Moore  246 

20  Aurora  260 

21  Summit  290    47 

22  Wornock  3 II     16 
Probable  error  of  a  single  observation  of  a  direction    (/?.   and  R.),  <',  =  zb  i" -27 

in  XVII  positions. 

Summit,  Blount  County,  Alabama.     October  20  to  27,  1877.     30'^"'  direction  theodolite  No.  loS.     F.  D 

Granger  and  J.  H.  Christian,  observers.     October  31  to  November  10,  1S7S.     Same  instrument, 

C.  O.  Boutelle  and  J.  B.  Boutelle,  observers. 


00  -GO 
19-77 
30-88 
04-41 
38  -60 
25  'II 
00  -66 
48-15 


-f  Q-II 

—  0-76 

—  0-27 

—  0-25 


04-52 

24  35 

00-93 

47-90 

Circle  used 


24 

Aurora 

25 

Wornock 

26 

Wilson 

27 

Rowe 

28 

Gunter 

Moore 

0    00 

00  -oo 

— o'39 

59-61 

117     35 

21  -57 

-^0-87 

22-44 

204    57 

48  -65 

—0  -04 

48 -61 

251     31 

08  -14 

-0  -03 

oSii 

292     24 

39-81 

—0-42 

59  39 

306    45 

30-51 

.... 

Probable  error  of  a  single  obsen'ation  of  a  direction  {D.  and  R.\  in  1877,  e\  =  =  i''''-2i,  and  in 
1S78,  ^,=  d=  i"  -35.     Circle  used  in  XVII  positions  in  both  years. 


' 


190 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directions  at  stations  coniposimj  the  second  section  of  the  triant^iilation  -west  of 

the  Atlanta  base  net,  iSj^-iSSj — continued. 

IVitson,  Morgan    Countj-,  Alabama.     June  28  to  July   25,  1S7S.     50'-'"    direction   theodolite  No.    113. 
C.  O.  Boutelle  and  J.  B.  Boutelle,  observers. 


Number 
of  direc- 
tions. 


Objects  observed. 


29 
31 


Resulting  directions 

from  adjustment 

of  first  section. 

Corrections 
from  adjust- 
ment of 
second  sec- 
tion. 

0 

/ 

// 

// 

0 

00 

00  •Del 

6 

20 

08  -64 

47 

10 

35-95 

-0  -35 

III 

24 

19 '56 

-0-51 

'50 

23 

34  -89 

+0  -87 

256 

06 

15  •2S 

352 

59 

40  'So 

Final 
seconds 


35 '60 
19 '05 
3576 


:  o'^  75.      Circle  used  in 


Sotnerville  Court-House 

Smithers 

Rowe 

vSunnnit 

Wornock 

Penit 

Capshaw 
Probable  error  of  a  single  ob.servation  of  a  direction  (/).  and  A'.), 
XI  positions. 

Wornoc/c,  Blount  County,  Alabama.  August  16  to  31,  1878.  50""  direction  theodolite  No.  113. 
C.  O.  Boutelle  and  J.  B.  Boutelle,  observers.  January  20  to  25,  1SS7.  30'^'"  repeating  theodolite 
No.  16.     O.  H.  Tittmann  and  J.  H.  Turner,  observers. 

o  /  // 

o     00     00  '00 

30       09       21  -57 

109     43     58  '02 

306       21       39-14 

334     25     29-11 

Probable  error  of  a  single  observation  of  a  direction  ( /).  and  A'. ),  <',  = 
XI  positions. 

Cheehahaiv,  Talladega  and  Clay  counties,  Alabama.     January  ;i  to  February  16,  1S86.     50""  direction 
theodolite  No.  114.     O.  H.  Tittmann,  J.  H.  Turner,  and  J.  E.  McGrath,  observers. 


34 

Sunnnit 

35 

Aurora 

36 

Cahaba 

32 

Wilson 

33 

Rowe 

-0  -98 

59-02 

-0  -20 

2t  -37 

-0-94 

58  -96 

-0-23 

38  -91 

-  0  -48 

29 '59 

9.     Circle  used  in 

37 
38 
39 


Horn 

Alpine 
Cahaba 
Aurora 
Indian 


o 

27 

63 

104 

J  60 


00       00  -QO 

39  56  -44 
41  15  -86 
45  29  -69 
19  03  -33 
Mean  correction 


— o  -19 
—  I  -03 
-f  I  -22 
o  -QO 
Circle 


15-67 
28  -66 


04-55 
used  in  -VII 


Probable  error  of  a  single  observation  of  a  directioti  ( />.  and  /?. ),  e,  ±o"-9t 
positions. 

Cahaba,  Saint  Clair  County,  Alabama.     March  8  to   31,   1886.     50'^'"  direction    theodolitt-    N",    1  14 
O.  H.  Tittmann  and  J.  E.  McGra^h,  ob.servers. 


40  'Wornock  o     00    00  -co 

41  Aurora  65     09     22  -94 

42  Cheehahaw  143  03  52  -83 
Alpine  171  08  59-72 
Laurel                                                                              217     19    44-87 

Mean  correction     o  oo 

Probable  error  of  a  single  observation  of  a  direction  (  D.  and  A". ),  ^'i  =  =bo"-99.     Circle  u.sed  in  VII 
positions. 


-0-4S 

59-52 

—0  -69 

22-25 

+  r  -16 

53  -99 

I 

II 
III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 

XIV 

XV 

XVI 

XVII 

XVIII 


No. 


THE    MAIN    TRIANGULATION. 

Ohscri'atio)!  equations. 


191 


o=--o77+  (6)~(i3)- 
o=-o-84+(i5)  -(14)- 
o=-i-8H  (i6)-(i5)-t 


o=+o-25  +  (24)-(2S)  +  (i7)    -(i6)  +  (i2)-(io) 


o=  +  o-82+(2o)-(i9)- 

O=+O-02-f-(2l)    -(19)  - 

o=-o-23-|-(3o)    -(29)+(23)-(2r)  +  (27) 
o=  +  o-29+(34)  -(32 

t)=— 2\S2 -1(31  )  — (29 

o=-2-o5  +  (35)-(34)+(25)  -(24)  +  (io) 
o=-o-64+(39)-(38)+   (7)-    (6)+   (2) 


(3)--  (2) 
(5)  (4) 
(4)    -    (3)  +  (i3) 


-(.2) 


i8)-(i6)+(r2)^-(ir) 

Hi8)-(i7)  +  (28)--(27) 

(26) 

(30-(3o)  +  (26)-(25) 

(23)-(22)  +  (33)-(32) 

(9) 
(r) 


o=-r50+(42)-(4i)+   (8)-   (7)  +  (38)-{37) 

o=-o78+(4i)-(4o)  +  (36)-(35)+   (9)"   («) 

o  =  +  i4-o+2-34(2)  +  2-5i (5 )H-2- 18 (6)  + 1 -49(12) -3-67(13)- 3-18(14) -4-23(15) -I -05(16) 

o=-f  2-8— i-96(io)H  2-4o(  11)— 0-44(12)  — 3-09!  16)^-4-93(17)  — 1-84(18)4-0-01(19)— 3-61(20) 

—3-62(21) 
o=  +  i-7-4-S4(2i)-f5-64(22)-o-So(23)-i-o2(29)-!-3-62(3Q)~2-6o(3i)-i-55(32)-4-4o(33) 

-2-85(34) 
o=  +  2-3-3-34(9)~.-5-74(io)  -2-40(11  )-3-6i  (20) --9-25(21  )     5/64(22)  -4-4o(33)-^8-o2(34) 

-3'62(35) 
o=  +  i7-4-o-76(i)+3-io(2)  +  i-oo(3)-i-i4(4)  — i-o5(i5)-i-3o(  16)  -o-25(  i8)-i-22(i9) 
+  2-94(  20) -I -72(22)- 1-44(33) -K I -S3  (35) -0-39(36) -2-42(37) -.-3-86(38) -I -44(39) 
-0-97(40)  + 1 -42(41) -0-45(42) 

Normal  equations. 
C5      C6      C^      Cs      C9     Cio    Cii    Cic    C,5        Cu  C,;  C16  Cir  Ci3 


=  -  0-77 

-  0-84 

-  I  -Si 

+  0-25 

-(-  0-82 

-I-    0'02 

-  0-23 
+  0-29 

-  2-82 

-  2-05 

-  o'64 

-  I  -50 

-  0-78 
+  1-1  -o 
+  2-8 
+  1-7 
-1-  2-3 
+  17-4 


C->      C3      C4 


+4 


+  4 


-l-fi 


—  2 

+  2 
+6 


—  2 

-1-2 

+6 


+  3-5' 

-  4  '90 

-t-  0-12 

-^  0-44 

+  0-44 


—  2 

4-6     -2 
+6 


+  2 
+  2 
4-6 


-   2-65 
+  9-54 
+   2-01      . 
— 10  -40   — 


-   1-96  + 


-     5  74 


4-84  + 

S-tSS  - 

7-52  + 

2-07  + 


.24 

■5<^ 


+6     -2 

+6     -2 
+6 


+  0-16 


+     0-2S 


+61  -32 


-  3  90 

+  73-17  + 

+  1 


'7-52  -  63 
06-66  —  iiS 

+  277 


I 


C,  =  -^-i  -079 
C2=  J-o  -526 

C3=+I   -076 
C4=-f  0-593 

Cs  =  -fo-[25 
Co  =  -1-0 -177 


Remit  111;^  eorielatcs. 
C;  =-i-o-i50 
Cs  =+0-107 
0,=  4-0 -361 
C,o= -1-0-980 
C,,  =  -f  0-727 
C,,=4-i  -on 


—  2  -10 
+  0-o-j 

+    0-21 

-  i-3'i 
J-   2 -61 

+  097 


+  028 
+  I -S3 

—  1-44 
+  4-41 
+  o-i: 
+  13  06 

+  7-04 

—  i6-a» 

—  I  -20 
+6o-o^-> 


C.5  = 

-*-o 

•S07 

Cu  = 

— 0 

-IS7 

C.s= 

-0 

0357 

C,6= 

— 0 

■153 

c.,= 

— 0 

•06S 

C.s= 

— 0 

■340 

I 


192 


THE    EASTERN    OBLIQUE    ARC. 


Resulting  Corrections  to  oliscrved  directions. 


(I)= 

=  -0-469 

(ii)  = 

=  -0-048 

(21)  = 

=  -fo  -267 

(31)  = 

=  +o-866 

(2) 

-I  -844 

(12) 

—0  -621 

(22) 

-0-255 

(32) 

—0-231 

(3) 

-0  '337 

(13) 

+0  -683 

(23) 

+0  -633 

(33) 

+0  -477 

(4) 

-to  -938 

(14) 

—  I  -121 

(24) 

-0  -387 

(34) 

—0  -982 

(5) 

+0  -057 

(15) 

-^o  -598 

(25) 

+0  -873 

(35) 

—0  -203 

(6) 

~o  -056 

(16) 

—  0  -170 

(26) 

-0  -043 

(36) 

f  0  -940 

(7) 

-0  -284 

(17) 

+  0  -240 

(27) 

—0  -027 

(37) 

-0-188 

(8) 

+0  -204 

(18) 

+0  "453 

(28) 

—0-416 

(38) 

—  I  -028 

(9) 

+0  -054 

(19) 

+0-113 

(29) 

-0  -355 

(39) 

+  1  -217 

(10) 

-f  0  -067 

(20) 

-0-759 

(30) 

-0-511 

(40) 
(41) 
(42) 

-0-477 
-0  -687 
+  1  -164 

Probable  error  of  an  observed  direction  o-6 


-V^- 


io""67. 


No. 


^suiting  angles  and  si 

des  of  tht 

sect 

md  section  of  the  tr 

iangittati 

on  'west 

of  the  Atlanta  t>ase 

net. 

stations. 

Observec 

angles. 

Correc- 
tions. 

Spheri- 
cal 
angles. 

Spheri- 
cal 
excess. 

Log.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

" 

// 

" 

// 

Aurora 

44 

06 

15-57 

-0-74 

14  -83 

2  -OO 

4-695 

837  9 

49 

640  -70 

Brandon 

93 

59 

16  -82 

-0-34 

16  -48 

2  -OO 

4-852 

202  7 

71 

154-56 

Indian 

41 

54 

32  -84 

+  1-85 

34  -69 

2  -00 

4-677 

999  5 

47 

643  -04 

Gunter 

33 

30 

43-00 

+  1  -72 

44-72 

I  -32 

4-573 

188  9 

37 

427  -34 

Gulf  Point 

39 

55 

42  -81 

+0  -06 

42  -87 

I  -32 

4  -638 

579  6 

43 

509  -05 

Brandon 

106 

33 

37-32 

—0-94 

36  -38 

I  -33 

4-S12 

764  0 

64 

977  -65 

Gunter 

63 

32 

43-50 

-0-77 

42-73 

I  -55 

4  677 

999  5 

47 

643  -04 

Brandon 

61 

36 

36-51 

+  1  -28 

37  -79 

'  -54 

4-670 

389  7 

46 

815-5' 

Aurora 

54 

50 

42 -Si 

+  1  -30 

44-11 

1  -54 

4-638 

579  6 

43 

509  -05 

Suiiiniit 

67 

35 

20-19 

+  0-03 

20 -22 

I  -I  I 

4-670 

389  7 

46 

815-51 

Gunter 

34 

15 

23-52 

+  0-41 

23-93 

I  -II 

4  -454  925   I 

28 

505  -27 

Aurora 

78 

09 

19 -86 

—  0  -69 

19-17 

I  -10 

4-695 

149  2 

49 

562  -05 

Rowe 

59 

59 

20  -70 

-0  -87 

19-83 

I  -28 

4-670 

389  7 

46 

815 -5> 

Gunter 

83 

07 

58-70 

+0-62 

59  -32 

1  -27 

4-729 

782  6 

53 

676-31 

Aurora 

36 

52 

45  -25 

-0  -57 

44  -68 

I  -28 

4-511 

•49  9 

32 

445-16 

Rowe 

90 

13 

56-25 

-fo-i6 

56 -4  r 

I  -02 

4  -695 

149  2 

49 

562  -05 

Gunter 

_       48 

52 

35  -iS 

+  0  -21 

35  -39 

'  -03 

4-572 

115  2 

37 

334  -92 

Suniniit 

40 

53 

31  -67 

-0-39 

31  -28 

I  -03 

4-5'r 

149  9 

32 

445  -16 

Summit 

108 

28 

51-86 

-0-36 

51  -50 

0-S5 

4-729 

7S2  6 

53 

676  -31 

Rowe 

30 

14 

35  -55 

+  1    03 

36  -58 

0-86 

4-454 

925  2 

28 

505  -27 

Aurora 

41 

16 

34-61 

—  0-T2 

34-49 

0-S6 

4-572 

115  I 

37 

334  -91 

Wilson 

64 

13 

43  -61 

—  0  -16 

43  -45 

0  '89 

4-572 

115  2 

37 

334  -92 

Rowe 

69 

12 

59  -34 

+  0-37 

59-71 

0  -89 

4-588 

392  3 

38  760-76 

Summit 

46 

33 

19-49 

-f  0  -02 

19-51 

0  -89 

4-478 

573  3 

30 

100-47 

THE   MAIN   TRIANGULATION. 


193 


No. 


14 


'5 


16 


Rcsuliini:;  aiiff/cs  and  sides  of  the 


!  tations. 

Wornock 

Rowe 

Summit 

Wornock 

Wilson 

Summit 

Wilson 

Rowe 

Wornock 

Wornock 
Rowe 

Aurora 

Wornock 

Sunnnit 

Aurora 

Cheehahaw 

Aurora 

Indian 

Cahaba 
Aurora 
Cheehahaw 

Cahaba 

Wornock 

Aurora 


second  section  of  the  ti'ianj^ulation 
l>asc  net — continued. 


west  of  the  Atlanta 


4192 — No.  7 — 02 


Ob.serv'et 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

r,oK.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

25 

34 

30  -89 

-  I  -46 

29-43 

069 

4-572 

"5 

2 

37  334  -92 

20 

29 

47-49 

-  0-52 

46  97 

0  -69 

4-481 

194 

5 

30  282  69 

133 

55 

46-57 

—  0  -90 

45-67 

0  -69 

4  -794  398 

5 

62  287-16 

53 

38 

20 '86 

-0-75 

20  •  1 1 

0-99 

4-588 

392 

3 

38  76rj-76 

38 

59. 

15-33 

+  1-38 

16  -71 

0-99 

4-481 

194 

6 

30  282  -70 

S7 

22 

27-08 

—0-92 

26-16 

I  "OO 

4-681 

98 1 

5 

48  aSi  -88 

103 

12 

58  -94 

-f  I  -22 

60-16 

I  -20 

4-794 

398 

5 

62  287-16 

48 

43 

11-85 

+  0-89 

12-74 

1  -19 

4-681 

981 

5 

48  081  -88 

28 

03 

49-97 

-to  -71 

50 -68 

I -19 

4-478 

573 

3 

30  100-47 

55 

43 

52-46 

-0-6S 

51-78 

2-19 

4-729 

782 

6 

53  676-31 

50 

44 

23  -04 

fo-50 

23-54 

2-19 

4-701 

488 

3 

50  290  -77 

73 

,■^1 

51  -36 

—0  -lo 

51  -26 

2  -20 

4-794 

398 

5 

62  287  -16 

30 

09 

21  -57 

4-0  -78 

22-35 

0-65 

4-454 

925 

I 

28  505  -27 

117 

35 

21  -57 

+  1  -26 

22-83 

0-64 

4-701 

488 

I 

50  290  -75 

32 

15 

1675 

4-0 -01 

16-76 

0-65 

4-481 

194 

4 

30  282  -69 

55 

33 

33  -64 

+  2-24 

35  -88 

3-97 

4-852 

202 

7 

71   154-56 

54 

20 

56-55 

-0-23 

56-32 

3-97 

4-845   763 

S 

70  107-39 

70 

05 

41  -09 

-1-37 

39-72 

3-98 

4-9<j9 

145 

I 

81   123  -21 

77 

54 

29  -89 

+  1-85 

31-74 

3-27 

4-909 

145 

I 

81   123  -21 

61 

01 

24  -61 

+  0-49 

25-10 

3-28 

4-860 

804 

4 

72  577  -90 

41 

04 

13  -83 

-  0  -84 

12-99 

3-28 

4  -736  436 

7 

54  505  -05 

65 

09 

22-94 

—0-21 

22-73 

1-34 

4-701 

4S8 

2 

50  290-76 

79 

34 

36  -45 

-t  I  -14 

37  -59 

I  -34 

4  -736 

436 

8 

54  505  -06 

35 

16 

''3 -85 

-0-15 

03-70 

I  -34 

4-505 

134 

I 

31  993  -83 

194 


THE    EASTERN    OBLIQUE    ARC. 


9.    THE    THIRD    SECTION   OF   THE    TRIANGULATION   WEST    OF   THE  ATLANTA  BASE  NET, 

ALABAMA,    1886-1890. 

This  section  forms  a  compact  figure  connecting  at  each  end  on  a  single  line  both 
with  the  preceding  and  the  following  sections.     It  covers  a  portion  of  the  valley  of  the 

No.  30.     Coosa    River   and    comprises  6 


Cahaho 


AI^BAMA 


'Weogu.fka, 


JcLmisoTL 


Kilometers 


I   M    Ul  Ul  U   M 


10 


10  20  30 

Statute  Miles 


40 


50 


t-l       I— I       U,!       I— I       U-l- 


10 


10 


20 


30 


stations,     who; 

5e     appro 

ximate 

heights  are  as 

follows: 

Meters. 

Feet. 

.\lpine 

473 

'    551 

Laurel 

4S0 

I   576 

Horn 

5SS 

I   930 

Kahatchee 

396 

I   300 

Weogufka 

352 

I    155 

Jamison 

255 

«35 

The  observers  emploj'ed 
almost  exclusivel}'  a  repeating 
theodolite  for  the  angular  meas- 
ures of  this  section.  In  the  ad- 
justment unit  weight  was  given 
to  all  directions.  The  mean 
closing  error  derived  from  the 
13  triangles  of  the  figure  ecjuals 


/23"4_ 


=  d=  i"'34  and  the  mean 

error  of  an  angle  —  zb  o" "  7  7 ,  aLso 
the  probable  error  of  a  direction 
I '34  _. 


=  0-674—^^  =±0  -37. 

The  observations  of  1888  at 
stations  Laurel  and  Horn  by 
As.si-stant  F.  W.  Perkins  were 
made  at  night  upon  lights. 
Subsequent  to  this  date  all  horizontal  measures  of  the  primary  triangulation  between 
these  stations  and  the  Gulf  coast  were  made  at  night  by  Assistants  F.  W.  Perkins  and 
W.  B.  Fairfield.  Advantage  was  thus  taken  of  the  greater  transparency  of  the  atmos- 
phere and  of  the  better  seeing  during  the  night  as  compared  with  the  day.  On  long 
or  difficult  lines  two  or  three  lights  arranged  vertically  were  shown  at  the  same  station. 


THE    MAIN   TRIANGULATION. 


195 


Abstracts  of  horizontal  directions  at  stations  composing  the  third  section  of  the  triani:;ulalion  west  0/ 

^Itlauta  base  net,  i886-i8()o. 

Ofd7/rt//rt?f',  Talladega  and  Claj'  Counties,  Alabama.     January  11  to  February,  16  1886.     50''"  direction 
theodolite  No.  114.     O.  H.  Tittniann,  J.  H.  Turner  and  J.  E.  ^IcGrath,  observers. 


Number  of 
directions. 


Objects  observed. 


Results  from  adjust- 
ment of  second 
section. 


Corrections 
from  adjust- 
ment of  third 
section. 


Final 
seconds. 


J             Horn                                                                                    o    00    00  "00            +0  "01  00  'oi 

2             Alpine                                                                                    27     39     56-44             —0-04  56-40 

Cahaba  6;,     41      15  '67  ....  

Cahdba,  St.  Clair  County,  Alabama.     March  8  to  31,  1886.     so"^"' direction  theodolite  No.  114.     O.  H. 

Tittmann  and  J.  E.  McGrath,  observers. 


o  00  59-52 

143  03  53  -99 

171  08  59-72 

217  19  44-87 

A /pine,  Talladega  County,   Alabama.      February  10   to  March   9,    1SS7.     3c 
No.  16.     O.  H.  Tittmann  and  J.  H.  Turner,  observers. 


Wornock 

Cheehahaw 

3 

Alpine 

4 

Laurel 

Number  of 
directions. 

7 

Horn 

8 

Kahatchee 

9 

Laurel 

Cahaba 

Cheehahaw 

objects  observed. 


Results  from  >tation . 
adjustment. 


-0-57 
—0-62 


60-29 

44  25 
repeating   theodolite 


Corrections 
for  third 
section. 


Final 
seconds. 


o    00    00  -00  ^o  -47 

79     16    54-51  -0-55 

131     56     48 -89  -0-34 

1 86    00    40  -66  —  o  -64 

301     54     18-60  —0-04 

Horn,  Talladega  and  Clay  Counties,  Alabama.     March  22  to  April  5,  1S87.     30""  repeating  theodolite 

No.  16.     O.  H.  Tittmann  and  J.  H.  Turner,  observers.     May  16  to  22,  18SS.  Instrument  as  before. 
O.  H.  Tittmann,  J.  H.  Turner  and  F.  W.  Perkins,  observers. 


00-47 
55  06 

4S-55 
40  02 
iS-56 


I 


13 

Alpine 

14 

Cheehahaw 

10 

Weogufka 

II 

Kahatchee 

12 

Laurel 

0 

00 

00-00 

-0-59 

59 '41 

94 

14 

22-53 

-fo  -03 

22-56 

260 

49 

34  -86 

-0  -27 

34  59 

29S 

04 

03  -82 

—0  02 

03 -So 

527 

42 

iS-it 

+0-S4 

iS-95 

Laurel,  Shelby  County,  Alabama.  May  it  to  28,  1887.  30'"'  repeating  theodolite  No.  16.  O.  H. 
Tittmann  and  J.  H.  Turner,  observers.  April  27  to  IMay  10,  1S8S.  Instrument  as  before.  P.  \V. 
Perkins  and  W.  B.  Fairfield,  observers. 


15 

Cahaba 

16 

Alpine 

17 

Horn 

i8 

Kahatchee 

19 

Weogufka 

Columbiana 

20 

Jamison 

0 

00 

00 -oo 

+0  -65 

00-65 

79 

45 

28  -59 

+0  -04 

28  63 

95 

31 

01  -66 

—0-40 

01  26 

124 

56 

26-94 

-0-33 

26-61 

147 

5>~-^ 

r6  -93 

—0  -06 

16  -87 

172 

5^1 

15  95 

17S 

28 

3>^  -93 

— o-io 

39  03 

196 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directions  at  stations  composing  the  third  section  of  the  triangulation  west  of 

Atlanta  base  net,  iS86-/Sgo — continued.- 


Kahatchct 


Number  of 
directions. 


25 

21 
22 
23 

24 


Talladega  County,  Alabama.     April    iS  to   2S,   1S87.     30^'"  repeating  theodolite  No.   16. 
O.  H.  Tittniann  and  J.  H.  Turner,  observers. 


Objects  observed. 


Jamison 

Columbiana 

Laurel 

Alpine 

Horn 

Weogufka 


Results  from  station 
adjustment. 


O  00  00  '00 

41  54  02  -20 

93  59  09-51 

176  08  20-52 

214  55  31 '04 

320  17  33  -35 


Corrections 

for  third 

section. 


+0-30 
-0-44 

— o  -04 
+0-I8 


Final 
seconds. 


09  -81 
20  -08 
31  -00 

33 '53 


IVeogiifka,  Coosa  County,  Alabama.  May  28  to  June  1  and  December  5  to  1888  to  January  17,  1889. 
30""  repeating  theodolite  No.  16.  F.  W.  Perkins  and  W.  B.  Fairfield,  observers.  Telescope  i"''9 
above  the  ground. 


28 

Kahatchee 

29 

Horn 

Wetumpka 

Wilder 

26 

Jami.son 

27 

Laurel 

0 

00 

00  -co 

-o-i8 

59-82 

37 

23 

29-76 

-f-0-20 

29-96 

164 

03 

00-15 

200 

00 

45-06 

260 

22 

41  -69 

— 0  -12 

41  -57 

336 

43 

24-84 

+0  -II 

24-95 

Mean  correction    o  -00 

Jamison,  Chilton  County,  Alabama.  February  i  to  March  5,  1889,  and  May  7  to  14,  1S90.  30"" 
repeating  theodolite  No.  16.  F.  W.  Perkins  and  W.  B.  Fairfield,  observers.  Telescope  2"''i 
above  the  ground. 


30 

Laurel 

31 

Kahatchee 

32 

Weogufka 

Wilder 

Perry 

I 

II 
III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 


0 

00      GO -00 

— Q-ig 

59-81 

32 

28      40  -43 

-f  0  -10 

40-53 

73 

08      57  -60 

+0  09 

57-69 

151 

38     56  '43 

231 

10     29  -86 

Mean  correction 

0-00 

0=  — 1-22+    (6) 

o=-i-o8+(i4)-(i3)+   (7) 
o=+2-ii+(i6)-(i5)+   (4) 


Observation  equations. 

5)+  (3)-   (2) 

(6)+    (2)-   (I) 

(3)+  (5)-  (9) 
o=  +  i-99+(22)-(2i)  +  (i8)-(i6)+  (9)^  (8) 
u=  +  o-ii  +  (23)-(22)-f  (8)~  (7)  +  (i3)-(ii) 
o=-i-55-f  (29)-{27)+(i9)-(i7)  +  (i2)-(io) 
o=-o-85+(29)-(28)  +  (24)-(23)  +  (ii)-(io) 
o=-i-o3-|-(3i)-(3o)  +  (2o)-(i8)+(2i)-(25) 
o=-fo-25+(32)-(3i)  +  (25)-(24)  +  (28)-(26) 
o=-o-67+(32)-(3o)  +  (2o)-(i9)  +  (27)-(26) 

o=-2-7-4.o2(i)+6-9i(2)+5-96(3)-2-o2(4)-3-33(i2)+3-i7(i3)-fo-i6(i4)-o-38(i5) 
+  7-84(i6)-7-46(i7) 


THE   MAIN   TRIANGULATION. 
Obaervalion  equations — continue'l. 


197 


XII     o=-o-4-ri3(rr)-t-3-33(  12) -2-20(13)  --5'37(  16) i-7'46(  17) -2-09(18) -o-29( 21) --2-91  (22) 
-2-62(23) 

XIII  o=+6-o-2-77(  10)  i-6-47(  I  i)-3-7o(r2)-3-73(i7)-i-8-68(i8)-4-95(i9)-4-«9(27) -7-65(28) 

--2-76(29) 

XIV  o=-3-i-3-39(i8)+4-95(i9)-r-56(2o)-^o-36(26)+4'S9(27)-5-25(2S) -3-31(30)^5-76(31) 

—2-45(32) 

Normal  equations. 
No.  Ci        C2        C3       C4       C5        C6        C7        Ca  C,  Ci,  C,i  Ci2  Ci,  C14 


I 

0=  — I  -22 

-f4 

—  2 

—  2 

_ 

0 

■95 

2 

-i-oS 

+6 

—  2 

+ 

7-92 

+ 

2    20 

3 

+  2-II 

+6 

—  2 

+ 

0 

■24 

- 

5-37 

4 

+  ■■99 

+6 

—  2 

—  2 

- 

7 

■84 

+ 

6-48 

+ 

8-68 

-     3  39 

5 

+  0  *II 

+6 

_2 

-1- 

3 

4 

■17 
13 

6-60 

6-47 
0.02 

6 

-1-55 

+  6          +2 

—  2 

+ 

— 

4-13 

_ 

+     006 

7 

-0-85 

+6 

—2 

+ 

I  49 

- 

I-I7 

+     525 

8 

-1-03 

+6 

—2 

+  2 

+ 

I  80 

- 

8-68 

-1-   10-90 

9 

+  0-25 

+6 

+  2 

+ 

7-65 

-   13-82 

10 

-0-67 

+6 

+ 

o-o6 

—     I  -12 

II 

-2-7 

+  241 

94 

- 

15  -82 

+ 

40-15 

12 

-0-4 

+  121  -48 

- 

65-60 

+     7-09 

13 

+  60 

+  267-03 

—  n8oo 

14 

-3'I 

+  140-17 

Resulting 

correlates. 

c, 

=-0 

•003 

C6=  + 

0 

-727 

c„= 

— 0 

•01 15 

c. 

=+0 

■034 

C7=- 

0 

•495 

c..= 

—  0 

•03S9 

C3 

=  -0 

•645 

C8=- 

-0 

-678 

C.3  = 

-fo 

-0134 

C4 

=-0 

•985 

c,=- 

-0 

■677 

Cx4= 

+0 

•01 84 

Cs 

=  — 0 

•437 

C,c=+o 

•S09 

Hesultinff  corrections  to  observed  directions. 


(l)  = 

=+0  -012 

(   9)  = 

=  -0-340 

(17)  = 

=  -0-399 

(25)  = 

=  — 0001 

(2) 

—0  -042 

(10) 

-0-269 

(18) 

-0  -334 

(26) 

—0-125 

(3) 

+0  -573 

(II) 

-0-015 

(19) 

-0-057 

(27) 

^o-io6 

(4) 

—0  -622 

(12) 

+0  -845 

(20) 

-i-o  -102 

(28) 

— OM76 

(5) 

—0  -642 

(13) 

-0  -593 

(21) 

4-0  -296 

(29) 

+0195 

(6) 

-0  -037 

(14) 

+0  -032 

(22) 

-0  -435 

(30) 

— 0192 

(7) 

+0-471 

(15) 

+0  -649 

(23) 

-0  -044 

(31) 

+0105 

(8) 

+0  -548 

(16) 

+0-041 

(24) 

—  0  -1S2 

(32) 

+0-087 

Probable  error 


of  an  observed  direction  o'Gjs    r^ — ^  — 

V     14 


^6. 


198 


THE    EASTERN    OBLIQUE    ARC. 


Resulting  angles  and  sides  of  the  third  section  0/  the  triangulation  ivcst  of  the  Atlanta  base  net. 


II       L 


13 


stations. 

Obse 

rved 

angles. 

Correc- 
tion. 

Spherical 
angles. 

Spherical 
excess. 

dista 

ices. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

Alpine 

115 

53 

37  -94 

-|~o  -61 

38-55 

1-38 

4  -S60 

804  4 

72 

577  -90 

Cahaba 

28 

"5 

0573 

+0-57 

06-30 

I  -37 

4-579 

566  6 

37 

981  -02 

Cheehahaw 

36 

01 

19-23 

+0-04 

19-27 

I  -37 

4-676 

196  3 

47 

445  -64 

Horn 

94 

14 

22-53 

T-o  -62 

23-15 

0-49 

4-579 

566  6 

37  981  -02 

Alpine 

58 

05 

41  -40 

+0-51 

41-91 

0-48 

4-509 

625  5 

32 

331  -47 

Cheehahaw 

27 

39 

56  '44 

—0  -05 

56-39 

0  -48 

4-247 

564  0 

17 

683  -33 

Laurel 

79 

45 

28  -59 

—0  -61 

27-98 

1-14 

4-676 

196  3 

47 

445  -64 

Cahaba 

46 

10 

45  -15 

—  I  -20 

43  -95 

1  -13 

4-541 

410  I 

34 

786  '45 

Alpine 

54 

03 

51  77 

-0-30 

51-47 

1-13 

4  -591 

4S2  6 

39  037  -55 

Horn 

32 

17 

41  -89 

-I  -44 

40-45 

0-39 

4  -541 

410  I 

34 

7S6  -45 

Laurel 

15 

45 

33  -07 

-0-44 

32-63 

0-39 

4-247 

564  0 

17 

683  -33 

Alpine 

131 

56 

48-89 

—0-81 

48-08 

0-38 

4-685 

086  5 

48  426  -88 

Kahatchee 

82 

09 

II  -QI 

-0-73 

ID  -28 

0-59 

4-541 

410  I 

34 

786  -45 

Laurel 

45 

10 

58  -35 

-0  -37 

57 -98 

0-58 

4  -396 

361  0 

24 

909  -27 

Alpine 

52 

39 

54-3S 

—0  -89 

53  -49 

0-58 

4-445 

918  0 

27 

920-17 

Kahatchee 

3S 

47 

10-52 

+0  -39 

ID  -91 

0-37 

4-247 

564  0 

17 

683  -33 

Alpine 

79 

16 

54-51 

-{-0  -qS 

54-59 

0-36 

4-443 

056  7 

27 

736  -82 

Horn 

61 

55 

56-18 

-0-58 

55  -60 

0-37 

4  -396  361  0 

24 

909  -27 

Kahatchee 

120 

56 

21-53 

-0  -34 

21  -19 

0-57 

4-685 

086  5 

48  426  -88 

Laurel 

29 

25 

25 -28 

+0-07 

25-35 

0-56 

4-443 

056  8 

27 

736  -83 

Horn 

29 

38 

14-29 

+0-86 

15-15 

0-56 

4-445 

918  0 

27 

920  -17 

Weogufka 

60 

40 

04-92 

+0-09 

05  -CI 

I  -66 

4  -685 

086  5 

48  426  -88 

Laurel 

52 

27 

15  -27 

+0-34 

15  -61 

I  -66 

4-643  871  6 

44 

042  -46 

Horn 

66 

52 

43  -25 

+  1  -12 

44-37 

1-67 

4 -70S 

307  5 

51 

086  -66 

Weogufka 

37 

23 

29-76 

+0-37 

30-13 

0-63 

4-443 

056  7 

27 

736  -82 

Kahatchee 

105 

22 

02-31 

+0-23 

02-54 

0-62 

4-643  871  6 

44 

042  -46 

Horn 

37 

14 

28-96 

+0-25 

29  -21 

0-63 

4-441 

562  6 

27 

641  -56 

Weogufka 

23 

16 

35-16 

—0-28 

34  -88 

0-47 

4-445 

918  0 

27 

920  -17 

Laurel 

23 

01 

49-99 

+0-28 

50-27 

0-47 

4-441 

562  4 

27 

641  -.55 

Kahatchee 

133 

41 

36-16 

+0-II 

36-27 

0-48 

4  -708 

307  5 

51 

086  -66 

Jamison 

32 

28 

40-43 

+0-30 

40-73 

0-99 

4-445 

918  0 

27 

920-17 

Laurel 

53 

32 

II  -99 

+0-44 

12-43 

0-99 

4  -621 

350  2 

41 

816-74 

Kahatchee 

93 

59 

09-51 

+0-29 

09  '80 

0-98 

4714 

9'5  2 

51 

869  -88 

Jamison 

40 

40 

17-17 

—0  -02 

17-15 

0-63 

4-441 

562  5 

27 

641  -55 

Kahatchee 

39 

42 

26-65 

-o-i8 

26-47 

0-63 

4-432 

911  3 

27 

096  -38 

Weogufka 

99 

37 

18-31 

—0-05 

18-26 

0-62 

4  -621 

350  2 

41 

816-74 

Jamison 

73 

oS 

57-60 

+0-28 

57-88 

I  -14 

4-708 

307  5 

51 

086  -66 

Laurel 

30 

30 

22  -GO 

+o-i6 

22  -16 

I  -14 

4-432 

9"  3 

27 

096  -38 

Weogufka 

76 

20 

43-15 

-fo-23 

43-38 

I  -14 

4-714 

915  2 

51 

869  -88 

THE    MAIN    TRIANGULATION. 


lo.  thp:  fourth  section  of 

THE  TRIANGULATION  WEST 
OF  THE  ATLANTA  BASE 
NET,  ALABAMA,   1888-1895.  ' 

The  triaiigulation  l)et\veen 
the  preceding  terminal  line 
and  the  southern  limiting  line, 
Creagh  to  Pollard,  follows  the 
valleys  of  the  Coosa  and  Ala- 
bama rivers.  It  is  abundantly 
supplied  with  check  lines, 
making  30  conditions  in  the 
adjustment.  The  linear  de- 
velopment is  209  kilometers 
(or  130  statute  miles).  The 
whole  of  the  scheme  lies  south 
of  latitude  33°  and  the  natural 
elevation  of  all  the  spurs  avail- 
able for  .stations  is  less  than 
220  meters  (or  722  feet); 
farther  south  the  ground 
slopes  gradually  to  the  level 
of  the  Gulf.  The  approxi- 
mate elevations  of  the  stations 
are  as  follows: 


Meters. 

Feet. 

Perry 

206 

677 

Wilder 

216 

710 

Wetunipka 

172 

565 

Parker 

170 

558 

Lowndesboro 

121 

396 

Mount  Carmel 

192 

629 

Lovers  Leap 

169 

556 

Bargenier 

I  78 

583 

Count}'  Line 

173 

56.S 

Ethridge 

143 

470 

Fatama 

165 

540 

Midway 

171 

562 

Creagh 

'33 

435 

Pollard 

121 

397 

The  observations  of  the 
primary  directions  were  made 
at  night  upon  lights  mounted 
over  the  respective  stations. 

At  Pollard  .station  it  was 
nece.ssary  to  mount  the  theodo 
lite    on    a    wooden     .structure 


199 


No.  31. 


We.ogu.fkcL 


K/amieoTX,, 


'y^e.tAjjmpha, 


FoTLcurd. 

Kilometers 


I  H  M  MH-H- 


10  20  30  40 

Statute  Miles 


50 


60 


hH    ^-1    v-i    1-1    1-^ 


10 


10 


20 


30 


40 


200 


THE    EASTERN    OBLIQUE    ARC. 


46'53  meters  (or  152  J^  feet)  above  the  ground,  in  order  to  raise  it  above  the  high  woods 
obstructing  the  hues  of  sight. 


Squaring  the  closing  errors  of  the  triangles  we  get  the  mean  error 


V  28  -^' 


•08 


I -08 


and  the  mean  error  of  an  angle —y^  =±o""63,  also  the  probable  error  of  a  direction, 
d=o"-30. 

Abslracls  of  horizontal  directions  at  stations  composing  the  fourth  section  of  the  triangulation  ivest  of 

the  Atlanta  base  net,  Alabama.  /SSS-/Sgj. 

Jamison,  Chilton  County,  Alabama.  February  I  and  March  5,  1889,  and  May  7  to  14,  1S90.  30*^™ 
repeating  theodolite  No.  16.  F.  W.  Perkins  and  W.  B.  Fairfield,  observers.  Telescope  2"''i  above 
the  ground. 


Number  of 
directions. 

Laurel 
Weogufka 

objects  obser\'ed 

3 

Wilder 

4 

Perry 

Corrections 
Results  from  adjust-  from  adjust- 
ment of  third  section.         ment  of 

fourth  section. 


Final 
seconds. 


O  GO  59  "81 

73  oS  57  -69 

151  38  56-43 

231  ID  29 '86 

Mean  correction 


-0-82 
+0-05 
-0-15 


55 '61 
29-91 


Weogufka,  Coosa  Countj-,  Alabama.     May  28  to  June  i,  and  December  5,  18S8,  to  January  17,  1889. 
30'^"'  repeating  theodolite  No.  i5.     F.  W.  Perkins  and  W.  B.  Fairfield,  observers. 


Kahatchee 
Wetumpka 
Wilder 
Jamison 


0     00     59  -82 

164   03   00-15 

+0-67 

00-82 

200    00     45  -06 

+0-14 

45-20 

260     22     41  -57 

Mean  correction 

+0-14 

Wilder,  Autauga  Count}',  Alabama.     June   13  to  July  28,  1890.     30"^"'  repeating  theodolite  No.   16. 
F.  W.  Perkins,  observer.     Telescope  20"'-3  above  the  ground. 


Number  of 
directions. 

objects  observed 

5 

Wetumpka 

Montgomery,  Capitol 

6 

Lowndesboro 

7 

Lovers  Leap 

8 

Parker 

9 

Perry 

10 

Jamison 

II 

Weogufka 

.esults  from  station 
adjustment. 

Corrections 
from  adjust- 
ment of 
fourth  section. 

Final 
seconds. 

0 

00 

00 

•00 

—0 

■32 

// 

0 

59 

•68 

36 
84 

00 

43 
39 

94 

■74 

05 

— 0 

•74 

39 

•00 

99 

41 

48 

-39 

—0 

-03 

48  -36 

145 

24 

54 

-49 

+  0 

-16 

54 

•65 

176 

38 

20 

-73 

+0 

-14 

20 

-87 

226 

24 

43 

-90 

+0 

•84 

44 

-74 

267 

32 

52 

■91 

—0 

-05 

52 

-86 

THE   MAIN   TRIANGULATION. 


20 1 


Abstracts  0/  horizontal  directions  at  stations  composing  the  fourth  section  of  the  triangulation  west  oj 
the  /Itlanla  Imse  net,  Alalmma,  /,S&V-/,?^5— continued. 

Perry,  Chilton  County,   Alabama.      July  30  to  Augu.st  6,    1890.     30""  repeatinj^  thcfKlolite  No.    r6. 
V.  W.  Perkin.s,  observer.     Telescope  i""7  above  the  j^round. 

Corrections 
Results  from  station      from  adjust-  Final 

adjustment.  ment  of  seconds, 

fourth  section. 


Number  of 
directions. 

objects  observed 

12 

Jamison 

13 

Wilder 

14 

Parker 

0      GO 

OfJ'fX) 

—0  '09 

59 -gi 

50     42 

04  "96 

"O  -06 

04-90 

96     51 

15-25 

--0-I5 

15-40 

Wetumpka,  Elmore  County,  Alabama.     March  6  to  May  23,  1892.     30'^"' repeatinj^  theodolite  No.  16. 
F.  W.  Perkins,  observer.     Telescope  i""8  above  the  ground. 

Off/  ff  ff 

00-30 


19 

Mount  Carmel 

Montgomery,  Capitol 

20 

Lownde.sboro 

21 

Wil 

22 

Weogut'ku 

II  -21 
35-29 
47-19 

Parlcer,    Autauga    County,    Alabama.      Augu.st   8   to   28,    1890.      30<^"'    repeating    theodolite   No.    16. 

F,  \V,   Perkins,  observer. 


0 

00 

00  '00 

+0-30 

15 

36 

22-25 

39 

09 

1 1  '09 

^0-I2 

97 

04 

34-94 

-^-0  -35 

48 

39 

47-96 

-0-77 

15 

Perry 

16 

Wilder 

17 

Lowndesboro 

18 

Lovers  Leap 

0 

DO 

00  -00 

—0-18 

59 -Sz 

102 

37 

25-30 

-0-17 

25-13 

172 

09 

44-08 

+0  -oS 

44-16 

203 

32 

39-76 

-0-27 

40-03 

Loivndesboro,  Lowndes  County,  Alabama.     March  26  to  April  25,   1892.     30^"^  repeating  theodolite 
No.  16.     F.  W.  Perkins,  observer.     Telescope  2o"'-3  above  the  ground. 


23 

Parker 

24 

Wilder 

25 

Wetumpka 

Montgomery,  Capitol 

26 

Mount  Carmel 

27 

Bargenier 

28 

County  Line 

29 

Lovers  Leap 

0 

00 

00  'OO 

— 010 

59  "90 

49 

oS 

27-40 

-^0-93 

28-33 

87 

07 

28-24 

-0-13 

28 -I  I 

lor 

49 

4S  -45 

171 

58 

00  -86 

—0  -20 

00  -66 

214 

iS 

04  -20 

-0  24 

03-96 

241 

53 

56  -76 

+  0-03 

56  79 

274 

05 

53  -00 

—0  -29 

52-71 

Mount  Carmel,  Crenshaw  County,  Alabama.     RLiy  26  to  June  i,   1892. 

No.  16.     F.  W.  Perkins,  observer. 


30™'  repeating  theodolite 


39 

Bargenier 

40 

Lovers  Leap 

41 

Lowndesboro 

Montgomery,  Capitol 

42 

Wetumpka 

0 

00 

00  -00 

^0  -39 

28 

34 

48  -68 

—0  -03 

56 

34 

1 2  39 

^001 

104 

47 

10-94 

112 

34 

33  92 

-0  -37 

00-39 
48 -65 

12  -40 

33  "55 


202 


THE    EASTERN    OBLIQUE    ARC. 


Ahslracls  of  horizontal  directions,  at  stations  composing  the  fourth  section  of  the  triangulation  xvest  of 
the  Atlanta  base  net.  Alabama,  iSSS-iSgj — continued. 


Lovers  Leap,  Lowndes  County,  Alabama.     June  4  to  20,  1892. 
W.  B.  Fairfield,  observer.     Telescope  7'""5  above  the  ground. 


Objects  observed. 


30"™  direction  theodolite   No.  135. 
Circle  used  in  XVII  positions. 


Nnniber  of 
directions. 

32 

Lowndesboro 

33 

Mount  Carmel 

34 

Bargenier 

35 

County  Line 

36 

Midway 

37 

Fatama 

38 

Ethridge 

30 

Parker 

31 

Wilder 

Results  from  station 
adjustment. 

Corrections 
from  adjust- 
ment of 
fourth  section. 

Final 
seconds. 

0 

/ 

// 

// 

// 

0 

00 

00  -00 

+0-04 

00-04 

49 

52 

45-80 

+0-55 

46  -35 

75 

30 

10-39 

—  0  -04 

10  -35 

115 

27 

55  "55 

+0  -II 

55-66 

142 

57 

02  -iS 

+0-I6 

02-34 

171 

54 

21  -51 

—0-34 

21-17 

1S5 

50 

02  -19 

—0  -09 

02  -10 

297 

17 

01  -14 

-0-31 

00 -S3 

330 

3S 

43-38 

-0  -08 

4,^  -30 

Probable  error  of  a  single  observation  of  a  direction  {D.  and  A".),  e^  =  ±  o'^-84. 

Ethridge,  Dallas  County,  Alabama.      June  6  to  11,  1892.      30""  repeating  theodolite  No.   16. 

Perkins,  observer. 


F.  W. 


00  -24 
26-61 
21    16 

Bargenier,   Lowndes    County,   Alabama.      March    18    to   April    7,  1892.      30"^'"  direction  theodolite 
No.  135.     W.  B.  Fairfield,  observer.     Circle  used  in  X^VII  positions. 


53 

Lovers  Leap 

54 

County  Line 

55 

Fatama 

0 

00 

CO  -00 

40-24 

51 

57 

27  -06 

-0-45 

153 

22 

20-95 

+0  -21 

43 
44 
45 

46 


County  Line 
Lovers  Leap 
Lowndesboro 
Montgomery,  Capitol 
Mount  Carmel 


0 

00 

GO  -00 

-(-0-29 

53 

59 

14-24 

+0-07 

98 

41 

16 -61 

-fo-2I 

132 

30 

40-19 

179 

47 

04-09 

-0-57 

Probable  error  of  a  sii:.gle  ob.servation  of  a  direction  {D.  and  R.),  c'l 


:o"-72. 


00  -29 

14-31 
16-82 


03-52 


County  Line,   Lowndes  County,  Alabama.     May  10  to  16,  1S92.     30""  direction  theodolite  No.    135. 
W.  B.  Fairfield,  observer.     Circle  used  in  XVII  positions. 


52 

Bargenier 

47 

Midway 

48 

Fatama 

49 

Ethridge 

50 

Lovers  Leap 

51 

Lowndesboro 

Probable  error  of  a  single  observation  of  a  direction  {D.  and  A'. ) 


0    00 

00  -QC 

-0-44 

59-56 

138   31 

49-80 

-0-27 

49-53 

177   24 

01  -35 

-fo-19 

01  -54 

216    16 

28  -96 

+0-38 

29-34 

273    56 

58-28 

—0-42 

57-86 

306    17 

06-94 

+0-56 

07  -50 

and  A'. ), 

t'.  =  ±  0" 

■87. 

THE   MAIN   TRIANGULATION. 


20' 


Abstrac/s  of  horizontal  directions  at  stations  composing;  the  fourth  section  of  the  trianf^ulation  -ucest  of 
the  .Itlanta  base  net,  /llabauia,  j8S8-/S(js — continued. 

Fatania,   Wilcox  County,  Alabama.     October    2   to  November  26,    1895.      30'"'  direction  theodolite 
No.  145.    G.  A.  Fairfield,  observer.    Telescope  I5"''8  above  the  ground.     Circle  used  in  XII  positions. 

Corrections 
Results  from  station        from  adjust-  Final 

adjustment.  ment  of  sections, 

jourth  section. 


Number  of 
directions. 

Objects  observed 

59 

Midway 

60 

Pollard 

61 

Creagh 

56 

Eth  ridge 

57 

Ivovers  Leap 

58 

County  Line 

0     00 

00  '(X) 

—0  -04 

59  96 

67     24 

iS-64 

-^0-33 

18  '97 

96     02 

10  '39 

—  0  '12 

10-27 

262     09 

32-81 

—0  "09 

32  72 

274     51 

31  72 

—  0  '11 

31  -61 

301      52 

12  -15 

—0-03 

12 -18 

and  R.  ] , 

e,  =  ±  0 

"•5.8. 

Probable  error  of  a  single  observation  of  a  direction  (D.  and  A".  ),  e^ 

Midway,  Monroe  County,  Alabama.     September  19  to  October   20,  1S95.      30-"'  repeating  thecKlolite 
No.  16.     F.  W.  Perkins,  observer.     Telescope  34""5  above  the  ground. 


62 

Pollard 

63 

Creagh 

Lookout  Hill 

64 

Fatama 

65 

Lovers  Leap 

66 

County  Line 

0 

00 

00  -GO 

-0-31 

59  69 

23 

41 

51  '42 

—  0-2I 

51  63 

50 

50 

15  -83 

82 

29 

45-86 

—Oil 

45  75 

148 

24 

01  -So 

—0  -10 

01  -90 

165 

29 

48-23 

+0-II 

48-34 

Creagh,  Clarke  County,  Alabama.     Augtist  9  to  September  10,  1S95.     30 '"  direction  theodolite  No.  1  ^5. 
G.  A.  Fairfield,  observer.     Telescope  i2'"-4  above  the  ground.     Circle  used  in  XVI  positions. 


White 

70 

Fatama 

71 

Midway 

72 

Pollard 

Red  Hill 

0 

00 

00-00 

196 

20 

14-53 

-0-30 

14  23 

221 

30 

12-95 

^0-41 

13  36 

270 

04 

55  -03 

— o-ii 

54-92 

320 

37 

14-96 

Probable  error  of  a  single  observation  of  a  direction  (/).  and  R.),  e,=  zt.o""]6. 

Pollard,  Monroe  County,  Alabama.     Augu.st  29  to  September  13, 1S95.     30""'  repeating  theodolite  No.  16. 
F.  W.  Perkins,  observer.     Telescope  46"'-5  above  the  ground. 


67 
68 
69 


Red  Hill 

White 
Creagh 
Fatama 
Midway  * 


0 

00 

00  00 

55 

52 

09  -60 

93 

01 

16-79 

—0  -01 

170 

38 

.48  -06 

-fO-I2 

200 

44 

46-47 

— o-ii 

♦The  correction  —  o"-09  was  applied  for  ecccniricity. 


16 

78 

48 

iS 

46 

36 

204 


THE   EASTERN   OBLIQUE   ARC. 


I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 

XIV 

XV 

XVI 

XVII 

XVIII 

XIX 

XX 

XXI 

XXII 

XXIII 

XXIV 

XXV 

XXVI 

XXVII 

XXVIII 

XXIX 

XXX 


=+I 

=     I 

=  — o 

=+I 

1  —  2 

=  — o 

=+o' 
=  +  r 
=  — o 

=  +r 
H-o 
=  +o 

=+I 

=  — o 
=  — o 
=  — o 

=  +o 

:— O' 

=  +o' 
=  +o' 
■—4' 

+o' 

=+3 

-3' 

+5' 

:  — I' 

+3' 

:-L2' 

—  I' 

=  +!■ 

+9' 

-6 

=  +5' 


Observation  equatio7is. 
•84-    (2)+   {3)-(io)  +  (ii) 

•92-    (I)+    (2)+    (5)-(ll)-(2l)+(22) 

•60-  (3)+  (4)-  (9)+(io)-(i2)+(i3) 
•19-   (8)+   (9)~(i3)  +  (i4)-(i5)^{i6) 

•24-     (5)+     (6)--(20)  +  (2l)-(24)+(25) 

•19-  (6)+  (8)-(i6)+(i7)-(23)+(24) 
•87-  (7)^  (8)-(i6)+(i8)-(3o)-f-(3i) 
•72-(i7)  +  (i8)i(23)- (29)^(30)+ (32) 
•63-(i9)-t-(2o)-(25)  +  (26)-(4i)+(42) 
•2i-(26)  +  (27)-(39)  +  (4i)-(45)+(46) 
•o2-(27)  +  {29)-(32)  +  (34)-(44)4-(45) 
•65-{33)+  (34)  -(39)  +  (4o)-(44)+  (46) 
o8-(34)  +  (35)"(43)+(44)-(5o)4-(52) 
•8o-(27)+(28)-(43)  +  (45)-(5i)+(52) 
69"(35)  +  (38)-(49)  +  (5o)-(53)+(54) 
97-(48)  +  (49)-(54)  +  (55)~(56)  +  (58) 
2o-(37)+(38)-(53)  +  (55)-(56)- 


61 -(47) 
09-(35)- 
33-(59) 
i4-(6o)- 

II-(62)- 


-(48)- 
-(36)- 
-(60)- 
-(61)- 
-(63)- 


-(5S)+(59)- 
-(47) +(50)- 
-(62)  +  (64)- 
-(67)  +  (6S)- 
-(67)-!-(69)- 


(64)4 

-(65)4 

(68)4 

(70)-! 


(57) 
(66) 
(66) 
(69) 
(72) 


(71)+ (72) 


3-2-90(1)4  4-10(2)  I  0-82(3) -0-39(4) -I -72 (12) +3-74(13) -2-02(14) +0-47(15) 

3i(i6)-o-78(i7)  — i-32(2o)+2-99(2i)  — i-67(22)-i-82(23)+4-52(24)  — 2-70(25) 

8  +  6-39(6)-7-54(7)-hri5(8)+o-78(i6)-4-23(i7)+3-45(  18) +1-08(30) 

74(3i)+2-66(32) 

0-0-22(5) +  7-76(6) -7-54(7) -2-58  (19) +3-90(20) -I -32(21) -3-74(31) 

52(32) -1-78(33) -3-96  (4o)+5-38(4r) -1-42(42) 

4-2-32(26) +3-55(27)-i-23(29)-o-55(32)+4-39(33)-3-84(34) -2-47(39) 

86(4o)-i-39(4i) 

3+2-80(27) -4-03(28) +  1-23(29) -1-0-55(32) -3-06(34) +  2-5 1 (35)  +0-15(50) 

55(5i)  +  i-4o(52) 

3-o75(35)+8-49(37) -7-74(38) -2-6i(48)+3-94(49) -1-33(50) -6-81  (56) 

35(57) -2-54(58) 

5  +  2-65(35) -4-o5(36)  +  i-4o(37)4-4- 13(57) -5-44(58)  +  i-3r  (59) +0-26(64) 

84(65)+6-58(66) 

6+0-87(59) -4-72(6o)+3-85(6i)+4-5i(62)-4-79(63)+o-28(64) +0-61(70) 

86(7i)  +  i-25(72) 


I 
i 


THE   MAIN   TRIANGULATION. 

Normal  equations. 


205 


'9 

0=+0  '09 

20 

-0-33 

21 

+0-14 

22 

+  0-II 

23 

-4-3 

24 

+  3 '8 

25 

+  6-0 

26 

-1-4 

27 

+  2-3 

2>S 

+  1-3 

29 

+  1-5 

30 

+  5-6 

C, 

C5 

C3 

C4 

Cs 

Cc 

C7 

Ce 

C9 

Ci  . 

Cii 

C.I 

c, 

C.4 

Cl^ 

C,', 

C.7 

Cl!^ 

I 

o=  +  i-84 

+  4 

—  2 

—  2 

2 

+  1  '92 

+6 

—  2 

3 

-I '60 

+6 

—  2 

4 

—  o'i9 

+6 

—  2 

-2 

5 

+  1  '24 



+6 

—  2 

—  2 



— 

6 

-2-19 

+6 

+  2 

—  2 

7 

-o'Sy 

+  6 

+  2 

8 

—072 

+6 

—  2 

9 

+0-63 

+6 

—  2 

10 

+  I-2I 

+6 

—  2 

+  2 

—  2 

II 

—  0'02 

+6 

+  2 

—  2 

+  2 

12 

+  1-65 

+6 

—  2 

13 

+o-o8 

+6 

+  2 

—  2 

14 

+o-8o 

+  6 

■5 

+  1  -69 

+6 

—  2 

+  2 

16 

-0-97 

+6 

+  2 

-2 

17 

—  0'20 

+6 

18 

—  o'6i 

+6 

Norvial  a/ nations — completed. 

C22  C23  C24  C2^  C26 


C27 


C28 


C25 


-  3-28 
+  2 '34 
+  4 '25 

-  5 '92 

-  2  91 
+  5 '25 

-  0-31 

-  I  '04 
+  1-38 


o'37 
6-39 
10-25 
6-54 
9 '26 


-     2-66 


276 
776 
3-80 
5 '52 
0-32 
5-38 
5 '52 


+  0-6S 

-  0-93 
+  6-95 

-  8-07 

-  I  '90 
+  3-84 

-  3 '55 


+  2 
+6 


2 'So 

5-i8 
3  06 
6-82 
3-SS 
2-36 


2-36 


+    0-58     +     2-65 


—  12  26 
+  10-82 

—  007 

—  007 

—  0-58 


+6 


—  2 
+6 


+2 
+  2 
+6 


-  2-65 

-  5  "44 
+  2-73 
+  13-07 
+  6-72 

-  1-05 


+  0-59 

-  9 -82 
+   9  21 

—  6-19 


-^92-50   +   3-54   -    9-10 

+  151-64     +I35'i' 
+234 '99 


—  1-46       +1  -46 

-33 '61       +  3 '04 

+  76-75       +19-87 

+45  94 


-      2-Ot> 
+  296-91 


+  6-65 
+  62-53 
+  163  -90 


+    I  -21 

+86 -61 


2o6 


THE    EASTERN    OBLIQUE    ARC. 


Resulting  correlates. 

Ci  =  — 0780  C„  =  +o'284  Coi  =  -|-o-242 

C:,=  — 0731  Ci2=— 0-249  C2,  =  — 0-237 

C3=+0-055  Ci3=+0-I0S  C23  =  +0"02l8 

C4  =  +o-i93  Ci4=— 0-397  0^4=— 0-00S6 

C5  =  — 0-418  Ci5=— 0-390  C25=+o-or83 

C6=+o-409  Ci6=+o-o58  €26=— 0-0760 

0;  =  — 0-043  Ci7=-ho-i55  C27= -0-1070 

Cg=+o-345  Ci8=+o-200  C28  =  — 0-0184 

C9=-o-345  C,9=+o-o67  C29  =  -o-o237 

C,o=- 0-326  C2o= +0-123  C3o=— 0-0944 

Rcsiillini:  CO!  rections  to  observed  directions. 


(0  = 

=  +0-668 

(19)  = 

=  +0-298 

(37)  = 

=  -0-344 

(55)  = 

=  +0-213 

(2) 

+0-138 

(20) 

+0  -116 

(38) 

-0  -093 

(56) 

—0  -088 

(3) 

-0-817 

(21) 

+0  -354 

(39) 

+0  -387 

(57) 

— 0-115 

(4) 

+0  -046 

(22) 

-0  -767 

(40) 

—0  -029 

(58) 

+0  -034 

(5) 

—0-317 

(23) 

—0  -104 

(41) 

+0  -012 

(59) 

—0  -036 

(6) 

-0  -739 

(24) 

-1-0  -926 

(42) 

-0-371 

(60) 

+0-327 

(7) 

—0  -03 1 

(25) 

-0-132 

(43) 

+0  -289 

(61) 

—0  -121 

(S) 

+0-163 

(26) 

-0-195 

(44) 

+0  -073 

(62) 

-0-312 

(9) 

+0-138 

(27) 

-0  -243 

(45) 

+0-213 

(63) 

+0-215 

(10) 

+0-835 

(28) 

+0  -034 

(46) 

-0-575 

(64) 

—0  -no 

(II) 

—0  -049 

(29) 

-0  -286 

(47) 

—0  -267 

(65) 

+0  -095 

(12) 

—0092 

(30) 

— 0-311 

(48) 

-rO-190 

(66) 

+0-HI 

(13) 

—0  -056 

(31) 

—0  -080 

(49) 

+0  -375 

(67) 

—0-005 

(14) 

+0  -149 

(32) 

+0  -039 

(50) 

-0  -423 

(68) 

+0-119 

(15) 

-0-183 

(33) 

^0-550 

(51) 

-0  -563 

(69) 

—0  -114 

(16) 

-0-173 

(34) 

-0  -037 

(52) 

-0  -438 

(70) 

—0  -300 

(17) 

+0  -083 

(35) 

+0-113 

(53) 

-ro  -235 

(71) 

+0-413 

(IS) 

+0-272 

(36) 

+0-163 

(54) 

-0  -448 

(72) 

-0-113 

Probable  error  of  an  observed  direction  0-674^ /^^  = 


=0  •34- 


Resulting  angles  and  sides  of  the  fourth  section  of  the  triangulation  zcest  of  the  Atlanta  base  net. 


No. 


Wilder 

Jamison 

Weogufka 

Wetunipka 

Wilder 

Weogufka 

Perry 

Jamison 

Wilder 

Parker 

Perry 

Wilder 


Observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

41 

oS 

09  -01 

—0  -88 

08-13 

0-81 

4-432  911  3 

27 

096  -38 

78 

29 

5874 

-0-S2 

57-92 

0-80 

4-605   982   4 

40 

362  -91 

60 

21 

56-51 

-0-14 

56-37 

o-8i 

4  -553  909  0 

35 

802  -14 

51 

35 

13-02 

—  I  -12 

II  -90 

I  -03 

4-605  9S2  4 

40 

362  -91 

92 

27 

07-09 

-0-27 

06-82 

I  -04 

4 -71 1  520  4 

51 

466  -00 

35 

57 

44 '91 

-0-53 

44-38 

I  -03 

4  -480  740  5 

30 

251  -06 

50 

42 

04  -96 

+  0-04 

05  -00 

I  -05 

4  -553  909  0 

35 

802  -14 

79 

31 

33 '43 

+0-86 

34-29 

I  -06 

4  -657  953  4 

45 

493  93 

49 

46 

23 '17 

+  0-70 

23-87 

I  -05 

4  -548  055  3 

35 

322  -81 

102 

37 

25 '30 

+0-01 

25-31 

0-68 

4  -657  953  4 

45 

493  '93 

46 

09 

10  -29 

-j-O  -21 

10-50 

0-67 

4  -526  629  6 

33 

622  -47 

31 

13 

26  -24 

-0  -03 

26  -2  1 

0  -67 

4-3S3  230  I 

24 

167  •4r 

THE   MAIN   TRIANGULATION. 


207 


A'esn/tivff  ang/es  and  sides  of  Ihr  fourth  section  of  the 

base  net — continued. 


triani^ulatiou  west  of  tlic  Atlanta 


No. 


13 


14 


15 


16 


stations. 

observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  <li.s- 
tances. 

Distance  in 
meters. 

0 

/ 

// 

// 

// 

// 

Lowiidesboro 

37 

5« 

60-84 

—  I  -06 

59  -78 

I  -06 

4  -480 

740 

5 

30 

251  06 

Wilder 

84 

05 

39  74 

-0  -42 

39-32 

I  -07 

4-689 

252 

3 

48  893  -63 

Wetuinpka 

57 

55 

23 -ss 

+  0  -24 

24  -09 

I  -06 

4-619 

619 

2 

41 

650  -40 

Lowndesboro 

49 

oS 

27-40 

+  1  -03 

28  -43 

I  -04 

4  -526  629 

6 

33 

622  -47 

Parker 

69 

32 

18  -78 

+0  -26 

19-04 

I  -04 

4-619 

619 

5 

41 

650  "43 

Wilder 

61 

19 

1475 

-t-o  -90 

'5  -65 

I  -04 

4-59' 

081 

3 

39 

00  r  -50 

Lovers  Leap 

33 

21 

42-24 

+0-23 

42-47 

I  -22 

4  -526  629 

6 

33 

622  47 

Parker 

100 

55 

14-46 

+0-45 

14-91 

I    23 

4  -778 

394 

I 

60 

033  -57 

Wilder 

45 

43 

06  -10 

+0-19 

06  -29 

1  -22 

4-641 

191 

1 

43 

771  -46 

Lovers  Leap 

62 

42 

58-86 

-fo-35 

59-21 

0-75 

4-591 

oSi 

3 

39 

001  -50 

Parker 

31 

22 

55-68 

-fo-ig 

55  -87 

0-75 

4  -358 

925 

0 

22 

852  -04 

Lowndesboro 

«5 

54 

07  -00 

^-o-IS 

07  -18 

0  -76 

4-641 

191 

2 

43 

771  -47 

Lowndesboro 

135 

02 

34 '4° 

+1  -21 

35-61 

0-57 

4  -778 

394 

I 

60 

033  -57 

Lovers  Leap 

29 

21 

16-62 

+  0-I2 

16-74 

0-57 

4-619 

619  4 

41 

650  -42 

Wilder 

15 

36 

oS  -65 

+0-71 

09-36 

0-57 

4-358 

924 

9 

22 

852  -04 

Mount  Carinel 

56 

00 

21  -53 

-0  -38 

21  -15 

I  -54 

4-689 

252 

3 

48 

893  63 

Lowndesboro 

84 

50 

32-62 

—0-07 

32  -55 

I  '53 

4  -768 

888 

I 

58 

733 -So 

Wetumpka 

39 

09 

1 1  -09 

—0-18 

10  -91 

I  -54 

4  -57" 

946 

7 

37 

234  -60 

Bargenier 

81 

05 

47  -48 

-0-79 

46  69 

0-66 

4-570 

946 

7 

37 

234-60 

Lowndesboro 

42 

20 

03-34 

—  0-05 

03  -29 

0  -67 

4-404 

518 

7 

25 

3S1  -59 

Mount  Carrael 

56 

34 

12-39 

-0-37 

12  -02 

0-67 

4-497 

668 

4 

31 

453  -46 

Lovers  Leap 

49 

52 

45  -So 

+o'5i 

46-31 

0  -70 

4-570 

946 

7 

37 

234-60 

Lowndesboro 

102 

07 

52-14 

—0  -09 

52-05 

0  -71 

4-677 

654 

I 

47 

605-17 

Mount  Carmel 

27 

59 

23-71 

+0-04 

23-75 

0  -70 

4  -35S 

924 

8 

22 

85  2  -03 

Lovers  Leap 

75 

30 

10-39 

—0  -08 

10-31 

0-52 

4-497 

668 

4 

31 

453  -46 

Lowndesboro 

59 

47 

48  -80 

—0-04 

48-76 

0-53 

4-44S 

35S 

9 

28 

077  -53 

Bargenier 

44 

42 

02-37 

+0-14 

02-51 

0-53 

4  -358 

924 

8 

22 

852  -03 

Bargenier 

125 

47 

49  -85 

-0-65 

49-20 

0-49 

4-677 

654 

I 

47 

605-17 

Lovers  Leap 

25 

37 

24  -59 

-0  -58 

24  -01 

0-49 

4-404 

51S  6 

25 

38 1  -58 

Mount  Carmel 

28 

34 

48  -68 

-o,-42 

48-26 

0-49 

4-448 

35S 

9 

28 

077  -53 

County  Line 

86 

03 

01  -72 

—0  -01 

01  -71 

0-34 

4  -448 

358 

9 

28 

077  -53 

Lovers  Leap 

39 

57 

45-16 

+0-15 

45-31 

0  -35 

4  -257 

120 

0 

iS 

076  -73 

Bargenier 

53 

59 

14-24 

—0  -22 

14  -02 

0  -35 

4  -357 

278 

3 

22 

765  -56 

County  Line 

32 

20 

08  -66 

+  0-99 

09  -65 

0-40 

4  -358  924 

9 

22 

S52  04 

Lovers  Leap 

115 

27 

55  -55 

+  0-07 

55  -62 

0-39 

4-586 

2S0 

5 

38 

572  "75 

Lowndesboro 

32 

U 

56-24 

-0-32 

55-92 

0-40 

4  -357 

278 

4 

22 

765  -56 

I 


20S 


THE   EASTERN   OBLIQUE   ARC. 


Resulting  angles  and  sides  of  the  fourth  section  of  the 

base  net — continued. 


j   Comity  Line 
17  \    Lowndesboro 
\   Bargenier 

f   Ethridge 
iS  \   Lovers  Leap 
\  County  Line 

j    Fatania 
19  \    Lovers  Leap 
I    County  Line 

{Fataina 
Ethridge 
County  Line 

I  Ethridge 
Lovers  Leap 
Fatania 

I  Midway 
Fatania 
County  Line 

{^Midway 
Fatania 
Lovers  Leap 

I  County  Line 
Midway 
Lovers  Leap 

I  Pollard 
Fatania 
Midway 

ICreagh 
Fatama 
Midway 

ICreagh 
Fatania 
Pollard 

(    Pollard 
28  I    Creagh 
[  Midway 


triangulaiion  -west  of  the  Atlanta 


Observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

Log.  di.s- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

53 

42 

53-06 

—  I  -00 

52-06 

0  -48 

4-497 

668 

4 

31 

453  -46 

27 

35 

52-56 

+0  -28 

52-84 

0-48 

4-257 

120 

I 

1 8 

076  -74 

yS 

41 

16 -61 

-0-08 

16-53 

0-47 

4  -586 

2S0 

5 

38 

572  -75 

51 

57 

27  '06 

-0  -68 

26  -38 

0-44 

4-357 

278 

3 

22 

765  -56 

70 

22 

06  -64 

—  0  -21 

06  -43 

0-45 

4-434 

99' 

6 

27 

226  -49 

57 

40 

29  -32 

—0-80 

28  -52 

0-44 

4  -387 

868 

6 

24 

426-92 

27 

GO 

40-43 

+  0-15 

40-58 

0-80 

4-357 

278 

3 

22 

765  -56 

56 

26 

25-96 

—  0-46 

25  -50 

0-80 

4  -620 

S73 

4 

41 

770  -86 

96 

32 

56  -93 

—  0  -61 

56-32 

0-80 

4-697 

224 

2 

49 

799-41 

39 

42 

39 '34 

-fo  -12 

39-46 

0  -60 

4  -434  991 

6 

27 

226-49 

lOI 

24 

53-89 

+0-66 

54-55 

0  -61 

4  -620 

873 

3 

41 

770  -85 

3« 

52 

27  -61 

+0-19 

27  -80 

0-60 

4-427 

241 

8 

26 

744  -95 

•53 

22 

20-95 

—0-02 

20-93 

0  -24 

4-697 

224 

2 

49 

799  -41 

13 

55 

40  -68 

+0-25 

40  -93 

0-25 

4-427 

241 

9 

26 

744  -96 

12 

41 

58-91 

—0-03 

58  -88 

0-25 

4-387 

868 

7 

24 

426  -92 

^3 

00 

02-37 

-fo-22 

02  -59 

0  -80 

4  -620 

873 

3 

41 

770  -85 

58 

07 

47 -85 

—0  -07 

47  -78 

0-79 

4-553 

155 

5 

35 

740  -08 

38 

52 

11  -55 

+  0-46 

12  -01 

0-79 

4-421 

772 

2 

26 

410-23 

65 

54 

15-94 

-jo  -21 

16-15 

1  -IJ 

4-697 

224 

2 

49 

799  -41 

85 

oS 

28 -28 

-|-o-o8 

28  -36 

1  -11 

4  -735 

254 

5 

54 

356  -87 

28 

57 

19-33 

-0-51 

18-82 

I  'II 

4-421 

772 

4 

26 

410-25 

135 

25 

08-48 

—0  -16 

08  -32 

0-49 

4-735 

254 

5 

54 

356  -87 

17 

05 

46-43 

+0  -02 

46-45 

0-48 

4-357 

278 

4 

22 

765  -56 

27 

29 

06  -63 

+0-05 

06-68 

0-48 

4-553 

155 

5 

35 

740  -08 

30 

05 

58  -41 

-0-23 

58-18 

I  -08 

4-421 

772 

3 

26 

410-24 

67 

24 

18-64 

+0  -36 

19  00 

I  -oS 

4-686 

818 

9 

48 

620  -44 

82 

29 

45  -86 

-|-0  -20 

46  -06 

I  -08 

4-717 

767 

0 

52 

211  -60 

25 

09 

58  -42 

+  0-71 

59-13 

1  -18 

4-421 

772 

3 

26 

410  -24 

96 

02 

10-39 

—0  -09 

10-30 

1  -19 

4-790 

720 

0 

61 

761  -81 

58 

47 

54-44 

—  0-32 

54-'2 

1  -18 

4-725 

276 

4 

53 

122  -24 

73 

44 

40-50 

+  0-19 

40-69 

'  -13 

4-717 

767 

0 

52 

211  '60 

28 

37 

51  -75 

-0-45 

51  -30 

I  -13 

4-415 

967 

I 

26 

059  -56 

77 

37 

3'  -27 

-|-0  -12 

3'  -39 

I  -12 

4-725 

276 

4 

53 

122  -24 

107 

43 

29-68 

— o-ii 

29-57 

1  -03 

4-790 

720 

0 

61 

761  -81 

48 

34 

42  -08 

-0-53 

41  -55 

I  -02 

4-686 

818 

9 

48 

620  -44 

23 

41 

51-42 

^0-53 

51-95 

I  -02 

4-415 

967 

I 

26 

059  -56 

THE    MAIN    TRIANGULATION. 


209 


CreagK 


II.    THE    FIFTH    AND    LA.ST  SECTION   OF  THE  TRIANGULATION    WEST   OF    THE    ATLANTA 
BASE    NET    AND   JUNCTION    WITH    THE    DAUPHIN    ISLAND    BASE,    I«95-l898. 

This  section  extends  to  tlie  Gulf  at  Mobile  Bay  and  no. 32. 

effects  the  junction  with  the  Dauphin  Island  base  line. 
It  is  composed  of  ten  stations  exclu.sive  of  the.  base 
stations,  and  presents  a  series  of  quadrilaterals.  The 
stations  are  of  very  moderate  height.  Their  approxi- 
mate heights  above  the  Gulf  level  are  as  follows: 


White 

Red  Hill 

Coon 

Dean 

Cokl  Creek 

Minette 

Spring  Hill 

Daphne 

St.  Elmo 

Fort  Morgan 

Dauphin  Island  East  Base 

Dauphin  Island  West  Base 


Meters. 

Feet. 

120 

393 

95 

3'l 

81 

265 

86 

284 

83 

274 

73 

240 

64 

210 

46 

152 

40 

132 

8 

27 

I 

3 

I 

3 

composing    the    figure    equa 


■^■^V^ 


I    T 


the 


The  country  being  well  timbered  and  cutting  im- 
practicable, it  was  necessary  to  elevate  the  theodolite  on 
scaffolds  ranging  from  i2""4  to  46'" "5  in  height,  with 
several  37'"  high.  All  observing  was  done  at  night  on 
signal  lights. 

The  mean  closing  error  derived  from  28  triangles 

28 

mean  error  of  an  angle  is  ±o"'6S,  and  the  probable 

I'ly 
error  of  a  direction,  o"674— 7=  =  d=o   '34. 

V  6 

For  the  several  sections  these  last  values  are  very 
nearly  equal  notwithstanding  the  number  of  observers, 
of  instruments,  and  methods,  and  other  circumstances, 
such  as  elevation  of  instruments,  day  or  night  observa- 
tions, etc.  The  values  of  the  probable  error  of  a 
direction  for  the  second,  third,  fourth,  and  fifth  sec- 
tions average  dro"'34,  which  indicates  that  the  tri- 
angulation  of  Alabama  is  of  a  high  degree  of  accuracy. 
4192  —  No.  7 — 02 14 


Cold 
CreeU 


St.  Elmo. 


DcLuphin 
Is  IcLixd.  BcLS  e 


Fort 
Morgan 


Kilometers 


o  10         20 

Statxite  Miles 


30 


10 


2IO 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directions  at  stations  composing  the  fift/i  and  last  section  of  the  triangulation 

west  of  the  Atlanta  base  net.  /Sgj-/SgS. 

Creagh,  Clarke  County,  Alabama.     Augvist  9  to  September  10,  1S95.     30™  direction  theodolite  No. 
135.     G.  A.  Fairfield,  observer.     Circle  used  in  XVI  positions.    Telescope  I2™'4  above  the  ground. 


Number  of 
directions. 


Objects  observed. 


Results  from  adjust-     Corrections  of         Final 
nient  of  fourth  section,      fifth  section.       seconds 


White 
Pollard 
Red  Hill 


o  00  00  "00 
270  04  54  -92 
320    37     14  96 


-o  '16 


-0-31 


00  '\(y 


15  "27 


/'()//<7;-(/,  Monroe  County,  Alabama.     August  29  to  vSeptember  13,  1S95.     30'-"' repeating  theodolite  No. 
16.     F.  W.  Perkins,  observer.     Telescope  46""5  above  the  ground. 


I 

Red  Hill 

2 

White 

Creagh 

0 

00 

00  "00 

—0  -40 

55 

52 

09  -60 

+0-17 

93 

01 

1678 

59-60 
0977 


White,  Clarke  County,  Alabama.     September  17  to  25,  1S95.     30'^'"  direction  theodolite  No.  145. 
Fairfield,  observer.     Telescope  27"''9  above  the  ground.     Circle  used  in  XII  positions. 


Objects  observed. 


G.  A. 


Number  of 
directions. 

5 

Creagh 

6 

Pollard 

7 

Red  Hill 

8 

Dean 

9 

Coon 

Results  from  station 
adjustment. 

Corrections 
from  adjust- 
ment of  fifth 
section. 

Final 
seconds. 

0        / 

00  '00 

-0-38 

// 

0     00 

59-62 

52     55 

48 '49 

^-o'i9 

48  -68 

116    57 

48  -60 

+  0'I2 

48-72 

141     23 

19  "31 

+0  '07 

19  •3« 

192     52 

41  -17 

0  '00 

41  -17 

Probable  error  of  a  single  observation  of  a  direction  [D.  and  A'.) ,  f,  =  ±0^-59. 

Red  Hill,  Baldwin  County,  Alabama.     July  21  to  24,  1895.     30""  repeating  theodolite  No.  16. 
Perkins,  observer.     Telescope  36"' '8  above  the  ground. 


F.  W. 


10 
II 
12 
13 
14 
15 


Dean 

Cold  Creek 

Coon 

White 

Creagh 

Pollard 


o  00  00-00 

26  51  17  -10 

67  01  49  -80 

124  29  52  -41 

148  09  19  -38 

184  35  44  -23 


-fo-17 
-0-31 

—  O  -22 
—0-13 

+0-31 
+  0-18 


Coon,  Washington  County,  Alabama.     August  7  to  20,  1S95.     30""  repeating  theodolite  No.  16. 
Perkins,  observer.     Telescope  3i"'-o  above  the  ground. 


00-17 
16-79 

49  ■5S 
52  -28 
19-69 
44-41 

F.  W. 


16 

17 
18 

19 

20 


White 
Red  Hill 

Dean 
Minette 
Cold  Creek 


O  00  00  -QO 

46  37  07  -81 

82  26  17-11 

loi  08  54-33 

129  46  38-59 


-t-o-i8 

o  -00 

—0-56 

+0-16 
-"-0-23 


00  -18 
07  -Si 
16-55 
54-49 
38-82 


THE    MAIN   TRIANGULATION. 


211 


Abstracts  of  horizontal  directions  at  stations  composing  the  fifth  and  last  section  of  the  triangtdation 
ivest  of  the  Atlanta  base  net,  /.S95-/<S9<?— continued. 

Dean,  Baldwin  County,   Alabama.     July  28  to  31,   1895.     30"^"  repeatinjj  theodolite  Xo.    16.     F.   W. 
Perkins,  observer.     Telescope  24"'"9  above  the  j^round. 


Number  of 
directions. 

Olijects  observed 

21 

Minette 

22 

Cold  Creek 

23 

Coon 

24 

White 

25 

Red  Hill 

esuUs  from  station 
adjustment. 

Corrections 
from  adjust- 
ment of  fifth 
section. 

Final 
seconds. 

0        / 

// 

// 

// 

0      GO 

0000 

--0-I5 

0015 

58     57 

45 '47 

— 0-14 

45 '33 

112     24 

09 '45 

+0  -48 

09  93 

15S     28 

36-00 

-0-65 

35-35 

1 89     33 

14-05 

+016 

14-21 

Cold  Creek,  Mobile  County,  Alabama.  December  i  to  9,  1S95.  F.  W.  Perkins  and  G.  A.  Fairfield, 
observers.  April  18  to  May  i,  1897.  W.  B.  Fairfield,  observer.  30^"'  repeating  theodolite 
No.  16.     Telescope  31'"  above  the  ground. 


26 

Coon 

27 

Red  Hill 

28 

Dean 

29 

Minette 

30 

Daphne 

Mobile,  Court-House  tower 

31 

Spring  Hill 

Minette,  B 

aldwin  County,  Alabama.     A 

o  00  00  "OO 

56  39  59-33 

79  13  14-83 

113  48  34-16 

156  54  45  -74 

1 78  09  04  -4 

191  47  54-07 


Fairfield,  observer.     Telescope  37""  above  the  ground. 


—0-24 
4-0-0I 
+0-42 
— o  -09 
— o  -lo 


32 


33 
34 
35 
36 


Daphne 

Mobile,  Court-House  tower 

Mobile,  transit  pier  (public  square) 

Spring  Hill 

Cold  Creek 

Coon 

Dean 


O  00  GO  -QO 

32  20  20  40 

33  02  05  -48 
45  32  20  -09 

loi  58  51  -79 

139  32  34  -86 

188  25  49  -05 


-0-37 


+0-45 

— 0-02 
+  0-15 
— O  -22 


5976 
59-34 
15-25 
34-07 
45-64 


54-07 

W.  B. 

// 

59-63 


20 

-54 

51 

■77 

35 

•01 

4S 

-S3 

Spring  Hill,  Mobile  County,  Alabama.     April  4  to  June  3,  1S97.     30'^^'"  repeating  theodolite 
W.  B.  Fairfield,  observer.     Telescope  37"'  above  the  ground. 


No.  16. 


37 
38 


39 

40 
41 


Cold  Creek 

Minette 

Mobile,  transit  pier 

Mobile,  Court-House  tower 

Daphne 

Middle  Bay  Light-House 

Fort  Morgan 

St.  Elmo 


0 

00 

00  -oo 

+  0-03 

00  03 

45 

34 

ri-13 

-0-49 

10-64 

82 

03 

45-44 

83 

20 

20-54 

103 

31 

00  -32 

—0-22 

00  -lo 

145 

I.X) 

31  '92 

156 

27 

50  -23 

-ro-2S 

50  51 

187 

37 

06  49 

+040 

06-89 

I 


212 


THE    EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directions  at  stations  composing  the  fifth  and  last  section  of  the  triangulation 
west  of  the  Atlanta  base  net,  iSg^-iSgS — continued. 

Daphne,  Baldwin  County,  Alabama.     May  4  to   15,  1897,  and  March  18  to  19,  1898.     30""  repeating 
theodolite  No.  16.     W.  B.  Fairfield,  observer.     Telescope  36'9  meters  above  the  ground. 


Number  of 
directions. 


Objects  observed. 


Results  from  station 
adjustment. 


Corrections 
from  adjust- 
ment of  fifth 
section. 


Final 
seconds. 


42 


43 
44 
45 


47 


Fort  Morgan 

Sand  Island  Light-House 

Middle  Bay  Light-House 

Dauphin  Island  East  Base 

St.  Elmo 

Spring  Hill 

Mobile,  Court-House  tower 

Mobile,  transit  pier 

Cold  Creek 

Minette 


o 

I 

13 

14 

55 

98 

III 

III 

140 

175 


51 


00       00  '00 

36     05  71 

14-53 
22  -41 

34-33 
47-03 
46  -96 

43  "93 
40  66 

3f^  -47 


+0-39 


00  '39 


—  I  •!! 

21  '30 

—0-03 

34  -30 

+0-32 

47-35 

-l-o  '04 

+0-40 


40-70 

3S-87 


St.  Elmo,  Mobile  County,  Alabama.  June  5  to  7,  1897,  and  January  31  to  February  iS,  1898.  30"'" 
repeating  theodolite  No.  16  in  1897  and  30^'"  repeating  theodolite  No.  32  in  1898.  W.  B.  Fairfield, 
observer.     Telescope  37*1  meters  above  the  ground. 


48 
49 

50 

51 
52 


Spring  Hill 

Daphne 

Middle  Bay  Light-House 

Fort  Morgan 

Sand  Island  Light-House 

Dauphin  Island  East  Base 

Dauphin  Lsland  -West  Base 

Point  aux  Pins  189S 


0 

00 

CX3  '00 

—0-30 

52 

46 

41  '22 

+0-04 

93 

42 

19-17 

130 

45 

49  -03 

H-O-22 

137 

29 

48  -87 

146 

48 

03-63 

0  '00 

167 

16 

23-72 

4-0-05 

192 

3S 

47-34 

59-70 

41  '26 


49-25 


03-63 
23-77 


Fort  Morgan,  Baldwin  County,  Alabama, 
repeating  theodolites  Nos.  16  and  32. 
the  ground. 


June  14  to  20,  1897,  and  January  20  to  24,  189S.      30"" 
■W.  B.   Fairfield,  observer.     Telescope  14-2  meters  above 


53 
54 


55 
56 

57 


Daujjhin  Island  West  Base 

Dauphin  Island  East  Base 

Baylor's  We.st  Base  1892 

Point  aux  Pins  1898 

St.  Elmo 

Spring  Hill 

Middle  Bay  Light-House 

Daphne 

Sand  Island  Light-House 


0 

00 

00  -GO 

+0-45 

8 

30 

12-65 

+0-23 

10 

02 

56-90 

27 

3« 

10-50 

55 

51 

43-92 

—0  -23 

73 

56 

39  -«6 

-0  -58 

89 

35 

36  -84 

102 

05 

04  -52 

+0-I4 

296 

55 

25-96 

00 

-45 

12 

•88 

43 

-69 

39 

•28 

04  -66 

THE    MAIN    TRIANGULATION. 


213 


^U)s/rac/s  of  horizontal  diiectious  at  stations  ioinposin}(  the  fifth  and  tast  section  of  the  triangiilation 
west  of  the  ^Itlanta  Imse  net,  /Sg^-zHgH — continued. 

Dauphin  Islajid  East  Base,  Mobile  Ccninly,  Alabama.     August  2  to  30,  1S97.     30'="'  repeating  theodo- 
lites Nos.  16  and  32.     W.  B.  Fairfield,  observer.     Telescope  2  V4  meters  above  the  ground  up  to 

August  27,  after  which  only  i4'2  meters. 


Number  of 
directions. 


Objects  observed. 


58 


Dauphin  Island  We.st  Base 

Point  aux  Pins  1898 

St.  Elmo 

Daphne 

Fort  Morgan 

Sand  Island  Light-House 

Danphin  Island  West  Base,  Mobile  County,  Alabama.  September  i  to  6,  1897,  and  February  23  to  27, 
1898.  30'"'  repeating  theodolite  No.  32.  W.  B.  Fairfield,  observer.  Telescope  23'4  meters  above 
the  ground. 


59 
60 
61 


Results  from  station 
adjustment. 

Corrections 
from  adjust- 
ment of  fifth 
section. 

Final 

seconds. 

0 

/ 

// 

// 

// 

0 

00 

00  '00 

+0  -23 

00  23 

46 

19 

52  -90 

80 

5' 

20  71 

—0  -08 

20-63 

125 

25 

47  ■<)9 

+  0  56 

47 '65 

197 

27 

36-9' 

-071 

36-20 

224 

55 

51  -14 

62 

63 
64 


I 

II 
III 

IV 

\' 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 

XIV 

XV 

XVI 

XVII 

XVIII 

XIX 


Casotte  1898 

Point  aux  Pins  1898 

St.  Ehno 

Dauphin  Island  East  Base 

Baylor's  West  Base  1892 

Fort  Morgan 

Sand  Island  Light-House 

Horn  Island  Light-House 


o 

46 

73 

151 

156 

l6<3 

174 
333 


Otiservation  equations 


o=— 0-56- 
o=-o-57- 

0=— Q-So- 
0=+0-2I 

o=  +  i-27- 
o=  +  r94- 
o=— 2-07- 
o=-o-57- 
o=+o-99- 
0= — 0-40- 
0=4-0-89- 
o=— 0-71- 
o=  — I•I7- 
o=— 1-31 
o=  — I■I4- 
o=  -0-13- 
0=4  0-46 
0=  —2-02- 
o=  — 1-69- 


•   (2)+   (4) 

-  (i)+  (3) 

■  (i)+   (2) 

■  (7)+   (9) 

-(I0)  +  (I2) 

-  (8)+   (9) 

■(l8)+{20) 
(II)  +  (I2) 
■(2l)+{22) 

(19) +(20) 

-(29)  +  (3i) 
(29)4  (30) 
■(32)  +  (33) 
(39)  4- (41) 
(39) +  (40) 
■(42)  +  (44) 
■(5o)  +  (52) 
■(53)+(54) 
(43) +  (44) 


-  (5)^  (6) 
-(i4)  +  (i5) 

-  (6)+  (7) 
-(i2)  +  (i3) 

-(i7)  +  (iS) 
-(i6)  +  (i8) 

-(22)+(23) 

-(i7)+(2o) 
-(28)  +  (29) 
-(26) +(29) 
-(33)  +  (34) 
-(32) +  (34) 
-(3S)  +  (39) 
-(44)  +  (45) 
-(42) +  (45) 
-(49) +(50) 
-(53)  +  (55) 
+  (58)-(6i) 

-(49)+(5i) 


-(I3)  +  (I5) 
-(i6)  +  (i7) 
-(23)-^(25) 
-(23)  +  (24) 
-(26) +(28) 
-(26)  +  (27) 
-(34)  +  (36) 
-(34)  +  (35) 
-(37) +  (38) 
-(46) +  (47) 
-(45)^(47) 
(48)  i  (49) 
-(56) +  (57) 
-(55)-r(57) 
-  (62)^(64) 
-(63)  +  (64) 
-(59)  +  (6o) 


00      GO  'OO 

29  59  '46 
25-29 
46-46 
30-71 
oS  -79 
48  -52 
03  -21 


+0-17 
-0-74 

+  0-56 


25 '46 
4572 


09 '35 


214 


XX 

o 

XXI 

o 

XXII 

o 

XXIII 

o 

XXIV 

o 

XXV 

o 

XXVI 

o 

XXVII 

o 

XXVIII 

o 

THE   EASTERN    OBLIQUE    ARC. 

Observaiioii  t'gnah'ons— continued. 

=  +  2-87-(42)+(43)-(54)  +  {57)-(6o)  +  (6i) 

=  -3-4-r43(i)+4-2i(2)  +  2-57(3)-2-57(4)-3-59(i3)+4-8o(i4)-r2i(i5) 

=  -i  •9+4-1 1  (7)-4-63  (8) +o-52(9)  +  i -99(16) -4-90(17) +  2-91  (iS)+o-48(  23  )-3-49(24) 

+  3'oi(25) 
=  -6-6+3'26(io)-4-i5(ii)+o-89(i2)  +  2-9i(i7)-4-85(iS)  +  i-94(20)-(-o-4o(26)-5-o7(27) 

+4-67(28) 
=  +5-4+4-28(i8)-6-22(i9)  +  i-94(2o)+o-4o(26)-3-45(28)+3-o5(29) +0-14(34)- 1 -84(35) 

+  170(36) 
=  -i-4-o-45(29)+3-o2(3o)-2-57(3i)-2-o7(32)+3-47(33)-i-4o(34)-i-S7(45)+2-37(46) 

-0-50(47) 
=  -4-7+o-22(39)-3-49(4o)+3-27(4i)  + 1 -43(42) -3-68(44) +2-25(45  )+4-43(55)-6-45(56) 

+  2-02(57) 
=  +  14-2-8-20(42) +10-59(43) -2-39(44)+o-i5(49)-t-7-33(5o)-7-48(5i)-2-o7(54) 

fi-94(55)+o-i3(57) 
=  -21 -8 +7-33(50) -12-97(51) +5-64  (52) +  14-09(53)  — 16-03(54) +1-94(55) +0-42(62) 

-i378(63)  +  i3-36(64) 


Noniial 

equations. 

No. 

Ci 

C2 

^■1 

C4 

Cs 

C6 

C7 

Cs 

C9 

Cio 

Ci, 

Cio 

Ci3 

C.4 

Cis 

C16 

C17 

C,8 

I 

0=^0  56 

-^4 

—  2 

2 

-0-57 

+4 

+  2 

3 

— o-8o 

+6 

—  2 

4 

+  0-21 

+  6 

—  2 

+  2 

—  2 

5 

+  1-27 

+6 

+  2 

-2 

+  2 

6 

+1-94 

+6 

—2 

7 

-2-07 

+6 

+  2 

—2 

+  2 

8 

-0-57 

+6 

+  2 

9 

+0-99 

+6 

+  2 

—  2 

—  2 

10 

— o'40 

+6 

—  2 

—  2 

11 

+0-89 

+6 

+  2 

-2 

12 

-0-71 

+6 

+  2 

13 

-I -17 

+6 

—  2 

—2 

14 

-i'3i 

+6 

+  2 

—  2 

15 

-I -14 

... 

... 

... 

+  6 

+  2 

16 

-0-13 

+6 

—  2 

17 

+0-46 

+6 

+  2 

18 

—  2 '02 

+6 

THE    MAIN    TRIANGULATION. 


21^ 


Noniial  equations — completed. 


19  o=—  I  -69 
+  2-87 

-  3 '4 

-  19 

-  6-6 
•+  5-4 

-  I '4 

-  4  7 
+  14-2 
-21  -8 


CI9 

Cio 

C21 

C22 

Cs3 

C»4 

C=5 

C26 

Ca, 

C28 

-  6-78 

—    2-01 

+    S-02 

+  4'1I 

1 

-  3 '59 

— 10  -48 
+  10 '34 
+   2  -10 
-  2-43 
+  4-90 

+    2  -02 
-10-13 

-  4-85 

+  n  -06 

-  I  -40 

-  4 '67 
+  I '54 

■f  4 '28 
+  4 '28 

-  6-19 
•f   1'54 
+  8-06 
+  8 -83 

-  2-91 

-  2-91 

+   0-95 
+   0-95 
-  6-99 

+   1-27 
+  6-91 

—     2  -03 

..- 

-2 

+  2 

-  1-87 

-  1-87 

+     8-9S 
+     5-58 

+      2-54 
+     8-33 

+  2 

+  2 
-2 

-     7-52 
+     4-43 

+   11-18 

-  5  39 

-  2  07 

+        5  39 

—  0-90 

-  2-98 

+6 

—  2 

+6 

+70 '37 

+96-51 

-  28-37 
+  112-07 

+  '2 '45 
-32-95 
-fS8-43 

-    f57 
+43  -58 

-  3-68 
+     0-59 

-  4-21 
+  10S-SS 

-  20-61 
+  20-99 

+     5  '93 
+302  -87 

-       12-97 
f       16  03 

+      8-59 
+   187-69 
+  1081-57 

C,  =+o-377 

C:=-fO'09I 

C4  =  - 0-363 

C5=  -O  -060 
C6=-  O  '40X3 

0,  =  — 0-014 
Cs=^o-i7i 
Cc;=— 0-I49 


Result inif  iomlates. 

C,c= +0-084 
C„  =  — 0-028 
C,2  =  — 0-063 
C„= +0-458 
C,4= +0-302 
C,5=+o-383 
C,6=-+-o-i77 

Ci7=-o-i59 
C,8=+o-230 


C,5=^o  -0S2 

C:  =  -0-479 

C.,  = -0-843 
Cii=  — o  -071S 
0,5  =  ^0-0325 
€,4=— 0-0387 
€35  =  — o  -0107 

C-6=-^  0-0307 
C:-  = -0-0563 

C2S  = +0-0367 


2l6 


THE    EASTERN    OBLIQUE    ARC 
Cort-ediofis. 


(I)= 

=  — o  -400 

(17)  = 

=  —0-005 

(33)  = 

=+0-449 

(49)  = 

=+0-035 

(2) 

+0  'iSS 

(18) 

—0  -560 

(34) 

—0  -016 

(50) 

^~0  -222 

(3) 

-l-o  -308  , 

(19) 

+-0-I57 

(35) 

+  0-155 

(51) 

—0  -003 

(4) 

+0  -160 

(20) 

-i-o  -229 

(36) 

—0-215 

(52) 

+0  -048 

(5) 

-0-377 

(21) 

-f  0-149 

(37) 

+0  -028 

(53) 

+0  -446 

(6) 

+0-189 

(22) 

-0T35 

(38) 

-0  -486 

(54) 

+0-229 

(7) 

^-o  -120 

(23) 

4-  0  -480 

(39) 

— 0  -220 

(55) 

-0  -230 

(8) 

+0  '068 

(24) 

-0-651 

(40) 

+0  -276 

(56) 

-0-581 

(9) 

0  'OOO 

(25) 

—0-156 

(41) 

+0  -402 

(57) 

-^0-136 

(lo) 

+0  -166 

(26) 

-0  -243 

(42) 

+0-392 

(58) 

i-o  -230 

(II) 

—0  -306 

(27) 

-j-o  •oob 

(43) 

-I -115 

(59) 

—  0  -082 

(12) 

—0  -223 

(28) 

Jo  -420 

(44) 

—0  -031 

,  (60) 

+  0-561 

(13) 

—0  '128 

(29) 

-  -0  -087 

(45) 

+0-316 

(61) 

-0  -709 

(14) 

+0-314 

(30) 

-0  -095 

(46) 

+0  -038 

(62) 

+  0-174 

(15) 

+0-I77 

(31) 

—0  "oor 

(47) 

+0  -400 

(63) 

—0  736 

(i6) 

+0  -180 

(32) 

-0  -373 

(48) 

—0  -302 

(64) 

J-O -561 

Probal)le  error  of  an  ol)serve«l  direction 


o  -674^^ 


:3_8 

28 


±  o"  -35. 


Resulting  angles  and  sides  of  the  fifth  and  last  seel  ion  of  the  triangnlatinn  -west  of  the  Atlanta  base  net. 


No. 


stations. 

Observer 

angles. 

0 

/ 

// 

White 

52 

55 

48  -49 

Creagh 

89 

55 

05-08 

Pollard 

37 

09 

07  -18 

Red  Hill 

36 

26 

24-85 

Creagh 

50 

32 

20  -04 

Pollard 

93 

01 

1678 

Red  Hill 

60 

05 

51  -82 

White 

64 

01 

60-11 

Pollard 

55 

52 

09  -60 

White 

116 

57 

48-60 

Creagh 

39 

22 

45-04 

Red  Hill 

23 

39 

26-97 

Coon 

46 

37 

07  -81 

White 

75 

54 

52-57 

Red  Hill 

57 

28 

02  -6  r 

Dean 

31 

04 

38  -05 

White 

24 

25 

30-71 

Red  Hill 

124 

29 

52-41 

Dean 

77 

09 

04  -60 

Coon 

35 

49 

09  -30 

Red  Hill 

67 

01 

49-80 

tion  ''^^'  "-'^' 

angles,    exce.ss. 


+0  -57  49  -06  o  -44 

+0-16  05-24  0-43 

—0-17  07-01  0-44 

— o  -14  24  -71  o  '75 

+0-31  20-35  0-75 

+0-40  07-18  0-74 

+0-30  52-12  0-78 

— o  -07  60  -04  o  -77 

+0-57  10-17  0-78 

+0  -49  49  -09  o  -47 

—0-15  44-89  0-46 

+0-44  27-41  0-46 

— o  -18  07  -63  o  -93 

~0-I2  52-45  0-92 

+0  -09  02  -70  o  -93 

+0  -81  38  -86  o  -54 

— o  -05  30  -66  o  -54 

-0-30  52-11  0-55 

—  o  -32  04  -28  o  -81 

—0-56  oS -74  o-8r 

-0-39  49-41  0-81 


Log.  dis- 
tances. 

Distances  in 
meters. 

4-415 

967 

1 

26 

059  -56 

4-514 

017 

4 

32 

660  -09 

4-295 

003 

8 

'9 

724  -40 

4-415 

967 

J 

26 

059  -56 

4-529 

S43 

I 

33 

872  -18 

4-641 

590 

9 

43 

811  -78 

4-514 

017 

4 

32 

660  -09 

4-529 

843 

I 

33 

872-18 

4  -493 

964 

7 

31 

186-36 

4-641 

590 

9 

43 

811  -7S 

4  -493 

964 

8 

31 

186  -37 

4-295 

004 

0 

19 

724-41 

4-493 

964 

7 

3' 

186  -36 

4-619 

293 

4 

41 

619-17 

4  -558 

422 

2 

36 

176-14 

4-493 

964 

7 

31 

186-36 

4-397 

629 

6 

24  982-14 

4-697 

157 

5 

49 

79T  -76 

4-619 

293 

4 

4' 

619-17 

4-397 

629 

5 

24 

982-13 

4-594 

429 

9 

39 

303  -38 

TPIE    MAIN   TRIANGULATION. 

Resulting  anglca  and  sides  of  Ihr  fiflh  and  last  section  of  the  Iriangnlation  -, 

Inise  wr/— continued. 


217 

vv/  of  the  Atlanta 


No. 


13 


14 


15 


16 


17 


iS 


19 


Coon 

White 

Dean 

Cold  Creek 

Coon 
Dean 

Cold  Creek 
Coon 
Red  Hill 

Dean 

Cold  Creek 
Red  Hill 

Minette 
Cold  Creek 
Dean 

Minette 

Coon 

Dean 

Cold  Creek 
Coon 

Minette 

Sprinj^'  Hill 
Cold  Creek 
Minette 

Daphne 
Cold  Creek 
Minette 
Daphne 
Sprinij  Hill 
Minette 
Spring  Hill 
Cold  Creek 
Daphne 
St.  Elmo 
Spring  Hill 
Daphne 
Fort  Morgan 
Spring  Hill 
Daphne 


Ohse 

rvt't! 

aiij^les. 

0 

/ 

// 

82 

26 

lyii 

51 

29 

21  -86 

46 

"4 

26-55 

79 

13 

'4  •«3 

47 

20 

21  -48 

53 

26 

23  -gs 

56 

39 

59 '33 

83 

09 

3078 

40 

10 

32  70 

13" 

35 

28-58 

22 

33 

15  "50 

26 

51 

17  -lo 

86 

26 

57  "26 

34 

35 

•9  "33 

5S 

57 

45  '47 

48 

53 

14-19 

18 

42 

37  '22 

ir2 

24 

09  '45 

I '3 

48 

34 '16 

28 

37 

44-26 

37 

33 

43  '07 

45 

34 

It  -13 

77 

59 

19-91 

56 

26 

3'  70 

34 

54 

57  -81 

43 

06 

> .  -58 

10 1 

5« 

5 1  79 

76 

30 

5'  -44 

57 

56 

49-19 

45 

32 

20  -09 

103 

3' 

tKl  -32 

34 

53 

"8  -33 

4' 

35 

53  "63 

52 

46 

41  -22 

84 

06 

06  - 1 7 

43 

"7 

12  -70 

28 

oS 

24-66 

52 

56 

49-91 

9^ 

54 

47  ""3 

Correc- 
tion. 


Spher-    Spher- 
ical ical 
angles,  excess. 


I^g.  dis- 
tances. 


Distances  in 
meters. 


')  -74  16  '37  r  '20 

— o  -07  21-79  '    '9 

—  I  -13  25  -42  I  -19 

+0-66  15-49  0-78 

+0  -79  22  -27  o  -79 

+0  -62  24  -60  0  -79 

+0-25  59-58  [-13 

+0  -24  31-02  I  -12 

-f-o  -oS  32  -78  r  -13 

-fo  -29  28  -87  o  -48 

+0-42  15-92  0-47 

—0-47  16-63  o '47 

-o  -20  57  -06  o  -35 

—0-51  18-82  0-36 

—0-28  45-19  0-36 

^0-37  13-82  0-52 

+0  -72  37  -94  o  -52 

+0-34  09-79  0-51 

+o'i6  34 '32  0-63 

1 0-07  44-33  0-63 

+0-17  43-24  0-63 


■'^97  157  5 
-594  430  « 
■558  422  3 

-594  429  9 
-468  673  o 
■507  C>02  9 

-619  293  4 
•694  251  8 
-507  002  9 

-694  251  8 
■397  629  6 
•468  673  I 

•468  673  o 
-223  609  6 
-402  402  o 

■594  429  9 
■223  609  8 
•6S3  316  4 

■6S3  316  4 
-402  402  o 
■507  003  o 


-0-51 

10 

■62 

0  -62 

4-402 

402 

0 

+0  -09 

20 

-00 

()-6i 

4  -539 

029 

5 

-0-47 

3 ' 

-23 

0  -62 

4 '469 

457 

8 

+0-36 

58 

■17 

0-63 

4  -402 

402 

0 

— 0  -01 

1 1 

■57 

0  -63 

4-479 

341 

0 

+0  -36 

52 

■15 

0  63 

4  '635 

156 

6 

+0  -08 

51 

■52 

0  -63 

4  '539 

029 

5 

+0-27 

49 

•46 

0-63 

4-479 

341 

0 

+0  -82 

20 

-91 

0  -63 

4-404 

704 

4 

-0  -25 

(X) 

-07 

0-61 

4  -635 

'56 

6 

1  Q-IO 

oS 

•43 

0  62 

4  -404 

704 

3 

-0  -28 

53 

'35 

0  62 

4-469 

457 

/ 

rO-34 

41 

•56 

0-47 

4  -404 

704 

4 

1  0  -62 

06 

■79 

0-46 

4  -3"i 

3 '3 

3 

+  0-35 

13 

•05 

0-47 

4  -338 

386 

5 

+0-72 

25 

•38 

0  -91 

4-404 

704 

4 

4  0  -50 

5''' 

•41 

0  -91 

4  -633 

149 

4 

-  o-o8 

46 

■95 

0-92 

4  -725 

827 

4 

49  79'  1'^ 
39  3'->3  -39 
36  176-15 

39  yi  -38 

29  422  -05 
32   136-82 

41  619  -17 
49  459  -74 
32  136-82 

49  459  '74 

24  982  -14 
29  422  06 

29  422  05 
16  734-38 

25  258-17 

39  303  -38 
16  734-39 
48  229  -90 

48  229  -90 
25  258-17 
32  136-83 

25  258-17 
34  596  -29 

29  475  -27 
25  25S17 

30  153-73 
43  167  -47 
34  596  -29 
3^*  '53-73 
25  392  -44 
43  '67-47 
25  392  43 
29  475  -27 

25  392  44 

31  719-28 
21   796-40 

25  392  -44 

42  968-43 
53   189-68 


2l8 


THE    EASTERN    OBLIQUE    ARC. 


Resulting  angles  and  sides  of  the  fifth  and  last  sections  of  the  triangulation  west  of  the  Atlanta 

base  net — continued. 


No. 


24 


25 


26 


27 


28 


Stations. 

Observed 

angles. 

Correc- 
tion. 

spner- 

ical 
angles. 

»pner 

ical 

excess 

0 

/ 

rr 

// 

// 

// 

Fort  Morgan 

46 

13 

20  '60 

+0-36 

20  -96 

0-96 

St.  Elmo 

77 

59 

07  '81 

+0-19 

08  -00 

0-95 

Daphne 

55 

47 

34  '33 

—0  -42 

33  -91 

0  -96 

Fort  Morgan 

iS 

04 

55  -94 

-0-35 

55-59 

0-51 

vSt.  Elmo 

130 

45 

49-03 

+  0-52 

49-55 

0-51 

Spring  Hill 

3' 

"9 

16-26 

+0-13 

16-39 

0-51 

Dauphin  Island  East  Base 

116 

36 

16  -20 

-0-63 

15  -57 

0  -26 

St.  Elmo 

16 

02 

14  -60 

—  0  -22 

14-38 

0-25 

Fort  Morgan 

47 

21 

31  '27 

—  0-46 

30-81 

0-25 

Dauphin  Island  West  Base 

.S7 

37 

43-50 

+  0-39 

43-89 

0-55 

St.  Elmo 

36 

30 

34-69 

—  0-17 

34-52 

0-55 

Fort  Morgan 

55 

51 

43  -92 

~o  -68 

43  -24 

0-55 

Dauphin  Island  We.st  Base 

78 

40 

21-17 

-  0-91 

20  -26 

0-27 

St.  Elmo 

20 

28 

20  -09 

+0-05 

20  -14 

0-27 

Dauphin  Island  East  Base 

.So 

51 

20  -71 

-0-31 

20  -40 

0  -26 

Dauphin  Island  East  Base 

162 

32 

23-09 

+0-94 

24  -03 

0-03 

Fort  Morgan 

S 

30 

12-65 

—0-22 

12-43 

0-03 

Dauphin  ]  sland  West  Base 

8 

57 

22-33 

+  1  -30 

23-63 

0-03 

Dauphin  Island  East  Base 

44 

34 

26  -38 

4-0-64 

27  -02 

0  -80 

St.  Elmo 

94 

ni 

22-41 

—0  -04 

22-37 

0  -80 

Daphne 

41 

24 

II  -92 

+ 1  -09 

13 -or 

0-80 

Dauphin  Island  East  Base 

72 

01 

49-82 

-I  -27 

48  -55 

0-41 

Daphne 

14 

23 

22  41 

-I  -51 

20  -90 

0-41 

F'ort  Morgan 

93 

34 

51  -87 

—0  -09 

51-78 

0-41 

Log.  dis- 
tances. 


Distances  in 
meters. 


4-501  323  ^  31  719-28 

4  -633  149  6  42  968  -45 

4-560  278  o  36  331  -05 

4-338  386  4  21  796-48 

4-725  827  4  53  189-68 

4-560  277  8  36  331  -03 

4-560  277  9  36  331  -04 

4-050  203  4  II  225-44 

4  -475  527  2  29  890  -09 

4-560  277  9  36  331  -04 

4 '335  134  2  21  633-87 

4-478  516  I  30  096-51 

4  -475  527  2  29  890  -09 

4  -027  831  9  10  661  -83 

4-478  516  o  30  096-50 

4-335  134  2  21  633-87 

4  -027  831  9  10  661  -83 

4  -050  203  5  1 1  225  -44 

4-501  323  3  31  719-28 

4  -654  020  6  45  083  -Si 

4-475  527  4  29  890-10 

4  -633  149  5  42  968  -44 

4-050  203  3  II  225-44 

4  -654  020  6  45  083  -81 


Remarks  on  the  accord  of  the  Atlanta  and  Dauphin  /s/and  Imses. — The  di.stance 
between  the  middle  points  of  these  bases,  when  measured  through  the  middle  line  of 
the  triangulation  connecting  them,  is  677  kilometers  or  421  statute  miles.*  The  total 
number  of  geometrical  conditions  demanded  by  this  triangulation  in  order  to  remove  its 
inconsistencies  is  142,  to  which  number  one  more  condition  would  hav^e  to  be  added  to 
bring  out  the  length  of  the  second  ba.se  as  measttred.  The  simultaneous  .solution  of  so 
large  a  number  of  equations  being  impracticable,  the  actual  adjustment  was  made  in 
parts.  -When  the  Dauphin  Island  base  was  reached  a  very  small  difference  f  was  found 
in  the  computed  length,  as  derived  from  the  Atlanta  base,  and  the  measured  length,  a 
matter  of  accident,  but  a  very  .satisfactory  one,  .since  no  further  labor  was  needed  to 
bring  about  a  closer  accord. 

*  It  is  made  up  of  the  several  parts  as  follows:  In  base  net,  42  kilometers;  first  section,  98  kilometers;  second  section, 
88  kilometers;  third  section,  80  kilometers;  fourth  section,  209  kilometers;  and  fifth  section,  160  kilometers. 
fOne  and  a  half  units  in  the  seventh  place  of  decimals  in  the  logarithm. 


THE    MAIN    TRIANGULATION. 


219 


12.    THE    FIRST   SECTION    OF    THE    TRIANGULATION   WEST    OF    THE     DAUPHIN    ISLAND 
BASE    NET,  ALABAMA    AND    MISSISSIPPI,    1846-1855. 

Proceeding  from  the  base  net  westward,  the  triangulation  is  contracted  in  dimen- 
sions and  possesses  an  inferior  degree  of  accuracy  as  compared  with  the  triangulation 
north  of  the  base.  This  change  is  primarily  due  t<j  unfavorable  atmospheric  conditions 
and  to  tlie  difBculty  of  preserving  the  stations  for  a  few  years  in  a  lo\v  country,  subject 
to  storms  and  severe  hurricanes,  which  cause  alterations  in  the  shore  line,  overflow  of 

No.  33. 


Deer  Jalaruil 


STiip  laXojrvdL 
1855 


Faint  aitx  JPirta 


Horn,  Island.  East 
2655 

Kilometers 


cLVLpnin.  lalcLTvfi, 
'We.st  ScLse 


Petit  Bcis 


10 


10 


20 


30 
Statute  Miles 


itO 


50 


60 


70 


10 


10 


20 


30 


<tO 


the  ground,  and  destruction  of  the  stations.  When  the  localities  were  revisited  in 
another  year  several  of  the  stations  could  not  be  recovered,  and  new  stations  had  to  be 
established  in  their  places.  The  width  of  the  triangulation  was  limited  by  the  width 
of  Mississippi  Sound,  along  which  it  extends.  The  observers  were  Assistants  F.  H. 
Gerdes  and  J.  E.  Hilgard.  In  1S54-55  a  Gambey  repeating  theodolite  was  used,  and 
for  the.se  measures  the  resulting  seconds  are  given  to  the  nearest  tenth.  The  .section 
extends  from  the  Dauphin  Island  base  net  to  the  line  Deer  Lsland  i  to  Ship  Island  1855, 
a  distance  of  about  56  kilometers  or  35  statute  miles.  The  connected  series  of  quadri- 
laterals terminates  here. 

Abstracts  of  horizontal  directions  at  stations  of  tlic  first  section  of  the  trians;nlaticm  west  of  Dauphin 

Island  base  net. 

Point  aux  Pins,  Mobile  County,  AlabaiDa.     May  and  June,  1S48.     F.  H.  Gerdes,  obser\-er. 
objects  obser\'ed. 


Number  of 
directions. 


Results  of  station        S'i":^,''^""^     Kesulting     S""^^!""''  Final 

adjusttuent.  ^1^^".,'^,?'        seconds'^      f~"''^^^         seconds. 


Cedar  Point 

Cat  Island 

Dauphin  Island  West  Base 

Petit  Bcis 

Grande  Batture 


o  /  // 

o     00     00  "OO 
22     36     33  '45 


5S 
I  OS 
147 


14     08-3 


.50 


51        21   -51 

05    47  69 


-005 
-003 


21    46 

47 -66 


-032 
— o  "29 
—0-03 


00  32 
33  16 
08-30 


220 


THE    EASTERN    OBLIQUE    ARC. 


Ahstrads  of  horizontal  direction  <.  at  stations  of  the  first  section  of  the  trianffulation  zcest  cf  /dauphin 

Island  Imse  net — continued. 

Dauphin   Island   West  Base,  Mobile   County,  Alabama.     November,  1.S47  and  January,  [848.    F.  H. 
Gerdcs,  observer. 


Number  of 
directions. 


Objects  Observed.  -^^l;;^--"      ^^^      ^^^    ^^  --.. 


Petit  Bois 
Grande  Batture 
Point  aux  Pins 


0 

00 

00  '00 

-0-I7 

59  "S3 

45 

15 

13 '69 

+0-36 

14  "05 

81 

33 

33 '52 

+0-14 


33-66 


Petit  Bois,  Jackson  County,  Mississippi.    June,  1846.     F.  H.  Gerdes,  observer.     Theodolite  No.  6  used 

in  III  positions. 


Horn  Island  East  1855  * 

Bayou  Casotte 

Grande  Batture 

Point  aux  Pins 

Dauphin  Island  West  Base 


0 

00 

GO -00 

-0-41 

42 

36 

12  -87 

+070 

71 

2.S 

26  -37 

—0  -64 

104 

36 

32-24 

+0-26 

155 

25 

46  '00 

+0-09 

59 '59 

13 '57 
25  73 
32-50 
46-09 


Grande  Batture,  Jackson  County,  Mississippi.  July,  1S46.  F.  H.  Gerdes,  observer.  45™  theodolite 
No.  4.  September  and  October,  1847.  J.  f;.  Hilgard,  observer.  Theodolite  No.  6  used  in  "V 
positions. 


10 

Point  aux  Pins 

0 

00 

00 -QO 

—0-06 

II 

Dauphin  Island  West  Base 

54 

50 

01  -60 

— o-iS 

12 

Petit  Bois 

i05 

37 

27-05 

+0-30 

13 

Horn  Island  Ea.st  1S55  * 

15S 

42 

11-77 

-0-39 

14 

Bayou  Casotte 

209 

13 

36-14 

4-0  -32 

59-94 

01  -42 

27-35 

11-38 

36-46 

Horn  Island  East  fS^j,  Jackson  County,  Mississippi.  February  and  March,  1847.  F.  H.  Gerdes 
and  J.  E.  Hilgard,  observers.  45""  direction  theodolite  No.  4.  ( V  to  X  positions.)  December, 
1854,  to  April,  1S55.     J.  E.  Hilgard,  observer.     Repeating  theodolite. 


21 
22 
23 
24 
19 
20 


East  Pascagoula 
Bayou  Casotte 
Grande  Batture 
Petit  Bois 
Horn  Island  West( 
Belle  Fontaine 


T847 


\   i«54-5 


0 

00 

00  '00 

+0-03 

14 

10 

58  -73 

+0  -12 

48 

41 

07-72 

+0-72 

104 

07 

58-38 

+0-33 

2S7 

05 

56-0 

—  1-02 

313 

55 

53-0 

—0  -19 

00-03 

58-85 
08  -44 
58-71 

54  -98 
52  -81 


Bayou    Casotte,    Jackson    County,    Mississippi.     Jvily   and    August,    1847.     F.    H.    Gerdes,    observer. 
Theodolite  No.  4.      (V  positions.)     September,  1847.     J.  E.  Hilgard,  observer.     Theodolite  No.  6. 


15 

Grande  Batture 

0 

00 

OQ-OO 

—0  -48 

16 

Petit  Bois 

47 

31 

37  -80 

+0  -75 

17 

Horn  Lsland  East  1855  * 

94 

58 

25-76 

—0  -64 

Horn  Island  West 

153 

29 

14  -20 

Belle  Fontaine 

180 

49 

13-30 

18 

East  Pascagoula 

202 

51 

05  -38 

+0-37 

59-52 

38 

-55 

26 

-12 

05-75 


*  The  observations  of  1847  were  reduced  to  the  position  of  1855. 


THE   MAIN   TRIANGULATION. 


221 


Abstracts  of  horizontal  dinrtioiis  at  stations  of  the  first  section  of  the  triani^utation  west  of  Dauphin 

[stand  base  net — continued. 

East  /'asatf^oiila,  Jackson  County,  Mississippi.  Auj^ust,  1847.  F.  II.  Genlcs,  oh^crver.  Tlieoflolite 
No.  4.  (  V  positions. )  April,  1854,  and  January,  1855.  J.  K.  Ililj^ard,  observer.  Repeating  the- 
oilolite.      Elevation  of  j^round,  16  feet;  of  tripod,  14  feet. 


Number  of 
directions. 

otijfcts  observed. 

25 

Bayou  Casotte 

26 

Petit  Bois 

27 

Horn  Island  East  1855* 

Azimuth  Mark 

28 

Horn  Island  West 

29 

Belle  Fontaine 

KesiiHs  of  station 
adjiistnieiit. 

o    /      // 

O   (K)   Of)  '(Xi 

20   42   28  -49 

57  56  20 -18 
96  22  50  '60 
25  'o 
i6-2 


122   43 

1 53  09 


Corrections 
from  first 
section. 


— o  '21 
—  I  '31 

4-o'26 

+0-65 
-^o  •61 


Final 
seconds. 


59  79 
27-18 
20-44 


25  65 
16 -81 


Horn  Island  West,  Jackson  County,  Missis.sippi.  August  to  November,  184S.  F.  H.  Gerdes,  observer. 
Repeating  theodolite.  March,  1854,  May  and  Novemlier,  1855.  J.  FC.  Hilgard,  observer.  Repeat- 
ing theodolite. 


32 
33 
34 


Ship  Island  1855 
Deer  Island  i 
Monk  Point 
Belle  Fontaine 
East  Pascagoula 
Horn  Island  Fla.st  1855 


30  Ship  Island  1855                                                                         o  00  00  -o  0-0            00-0 

31  Deer  Lsland  I                                                                                 54  48  36-8  —0-7             361 

7«  59  i«-8               

100  06  34-9  +0-3            35-2 

153  53  6<j-2  -0-5            59-7 

196  12  49-2  —0-9            50 'I 

Belle  Fontaine,  Jackson  County,  Mississippi.     April,  October,  and  November,  1S55.     J.  E.  Hilgard, 

observer.     Repeating  theodolite. 


35 
36 
37 
38 
39 


East  Pascagoula 
Horn  Island  East  1S55 
Horn  Island  West 
Ship  Island  1855 
Deer  Island  i 


o 

38 
95 
147 
191 


00 
42 
46 
26 
39 


// 
00  -o 
55-8 
44  o 
07-2 
39'' 


-0-7 

-+-0-4 

o  -o 

o  -o 

--0-4 


59 '3 

56-2 
44  o 

07  -2 

39  "5 


Ship  Island  1S55,  Harrison  County,  Mississippi.      June  and  July,  1S4S.      F.  H.  Gerdes. 
theodolite.     November,  1855.     J.  E.  Hilgard,  observer.     Repeating  theodolite. 


Repeating 


40 
41 

42 


Cat  Island 
Mississippi  City 
Biloxi  Light 
Deer  Island  1 
Belle  Fontaine 
Horn  I.sland  West 
Chandeleur  Light  1S55 


0 

00 

00  0 

49 

20 

56  9 

87 

13 

41-8 

11.6 

14 

■17 

+0-5 

12  -2 

1 48 

10 

5'-'  '2 

—  I  0 

49 -2 

176 

24 

5"  7 

-+0-5 

51  '2 

26S 

06 

00 -s 

*  Observations  of  1S47  referred  to  the  position  of  1S55. 


222 


THE   EASTERN    OBLIQUE    ARC. 


Abstracts  of  horizontal  directions  at  stations  of  the  first  section  of  ttie  trianffulation  zaest  of  Dauplnn 

Island  base  net — continued. 

Deer  Island  /,  Jackson  Connty,  Mississippi.     October,  November,  and  December,   1855.     J.  E.  Hil- 

gard,  observer.     Repeating  theodolite. 


iNumDer  01 
directions. 

Objects  observed 

43 

Belle  Fontaine 

Monk  Point 

44 

Horn  Island  West 

45 

Ship  Island  1855 

Mississippi  City 

Biloxi  Light 

.esults  of  station 
adjustment. 

Corrections 

from  first 

section. 

Final 
seconds. 

0 

r 

ff 

// 

// 

0 

00 

00  'O 

+0-I 

DO  "I 

0 

19 

13-2 

38 

49 

057 

+  0-I 

05 -s 

103 

49 

51  -4 

—  OT 

51  -3 

174 

34 

46  T 

194 

35 

56-5 

I 

II 
III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 

XII 

XIII 

XIV 

XV 

XVI 

XVII 

XVIII 


Observation  equations. 

0=^174- (i)  +  (2)-(7)  +  (9)-(ii)  +  (i2) 
o=-o-5i-(2)  +  (4)-(io)  +  (ii) 
o=-i-28-(3)  +  (4)-{7)  +  (8)-(io)  +  (i2) 
o=+o-o9-(6)+(7)-(i2)  +  (i4)-(i5)  +  (i6) 
o=+o-o7-(5)  +  (6)-(i6)  +  (i7)~(22)+(24) 
o=-i-i5-(i3)  +  (i4)-{i5)  +  (i7)-(22)  +  (23) 
o=-r57-(i7)  +  (i8)-(2i)  +  (22)-(25)  +  (27) 

o=-ro-(i9)  +  (2o)-(32)+(34)-(36)+(37) 

o=-i7-(2o)4-(2i)-(27)  +  (29)-(35)+(36) 

o=+o-i-(2S)  +  (29)-(32)  +  (33)-(35)  +  (37) 

o=  +  ro-(3o)  +  (3i)-(4o)  +  (42)-(44)  +  (45) 

o=-i-4-(3i)-r(32)-(37)  +  (39)-(43)+(44) 

o=  +  r4"(3S)  +  (39)-(4o)  +  (4i)~(43)+(45) 

o=+4-8+2-o9(i)-4-95(2)-2-4o(3)+2-36(4)+3-oo(7)-3-22(8)+o-22(9) 

o=+8-2+2-29(5)— 6-ii(6)+3-82(7)  -0-51(12)  — i74(i3)-t-2-25(  14 )+3-o5(22) -3-06(23) 

+0-01(24) 
o=— 4-84+0-229(5)— 0-229(6) +3-035(16) -3-035(18) -1-0-834(21  )-o-835(22)-f  0-001(24) 

+3'46(  25) -3-592(26) +0-132  (27) 
o=+2-o+4-i7(i9)— 6-20(20) +2-03(2  r)— 0-19(27)— 3-58!  28) -f-3-77  (29) +1-76(32) -I -54(33) 

—0-22(34) 
o=-9-o^  I -49(3o)-3-57  (31) -1-2-08(32) -0-22  (37)  -2-i6(38)+2-3S(39) +2-i7(4o)-3-38(4i) 

+  1-21(42} 


THE   MAIN   TRIANGULATION. 


223 


No. 

I 

o=-i74 

2 

o=+o-5i 

3 

o=-i-28 

4 

o=+o'09 

5 

o=+o'07 

6 

o=  — I  '15 

7 

o=-i-57 

8 

0=  — I  '0 

9 

o=-i7 

10 

o  =  +o'i 

II 

0=  +  I  '0 

12 

0==  — I  '4 

13 

o=  +  i-4 

14 

o=+4-8 

15 

o=+8-2 

16 

o=— 4  '84 

■7 

0=+2  '0 

18 

o=— 9'0 

Normal  equations. 
Ci    Co     C;i    C,    Cr,    C„    C;    Ck    C.J     C,„  C,,     C,,       C,,  C,, 


+6   —2   +2   —2 
+4   +2 

+6  -2 

+  6    -2    +2 

+6+2 

+6 


+6 


—  2 
+6  -2  +2 

+6   +2 
+6 


+  6 


+6 


ReaitHiiii:;  iorrr/ates. 


C,  =  +o  -0965 
C2=— o  "0831 
C3=+o-i404 
C4=  -0-0306 
C5  =+o-3323 

C6= +0-5085 

C7=-+i  -4771 
Ca  = +0-8785 

0,=  +!  -2697 


C„= -0-5309 
C„  =  +o-255i 

C„= -^0-3376 

C,3=— 0-4014 
C,4=— O  -03628 
C,5  =  — 0-06853 
C, 6  =+0-36560 
C,7=— O  -03300 
C,8=-  0-17487 


C,- 


-  9-82 

-  4-33 

+  7-3' 

—  I  -46 

-  4-33 

+  3-0" 

+ 1 2  -69 

+ 

3-264 

-11-44 

- 

2-658 

-  212 

+ 

0-834 

+  3-05 

" 

8-031 

-   2-22 
-12-35 

-  2-30 

+ 

0-702 

+  1219 
+  4-05 

-  2  30 

+  2 

-  6  02 

+  2 
+6 

+   1-76 

+  8-25 
—   I  01 

+59 '617 

+  11-46 



+84-185 

- 

0  -6201 

+44  -8ojg 

+   1  -6679 

+92-532^ 

-1-  3  6608 

+47-2672 

Resiiltini^  conrciioiis  Id  ohserz'ed  direc/ior/s. 


(i)  =  -o-i} 


■ 

I 


(2) 

+0  -359 

(3) 

-0  -054 

(4) 

—0  -02S 

(5) 

--0  -406 

(6) 

+0-698 

(7) 

-0  -638 

(8) 

+0-257 

(9) 

+0  -088 

(10) 

-0  -057 

(11) 

— q  -180 

(12) 

+0  -302 

(13) 

-0  -3S9 

(14) 

+0-324 

('5) 

-0  -47S 

(16)- 

=  ^0-747 

(31)  = 

=  -0-707 

(17) 

—0  -636 

(32) 

—0  -296 

(iS) 

-TO  -367 

(33) 

—0  -480 

(19) 

I   -016 

(34) 

+0  -886 

{20) 

—  0  -187 

(35) 

-0  -739 

(21) 

+  0  -030 

(36) 

+0  -391 

(22) 

-*  0  -122 

(37) 

—0  -02S 

(23) 

4-0-718 

(3S) 

+0  024 

(24) 

-0-352 

(39) 

+0  -352 

(25) 

~0  -212 

(40) 

4-0  -526 

(26) 

'   ■313 

(41) 

-0  992 

(27) 

■   0  -261 

(42) 

+0  -467 

(28) 

•   0  -649 

(43) 

^0  -064 

(29) 

-0-614 

(44) 

— 0-0S4 

13"^ 

-0  -005 

(45) 

—0  -146 

Probable  error  of  .111  ol)serveil  ilirection 


^         /ii  -28  ,, 


I 


124 


THE    EASTERN    OBLIQUE    ARC. 


A'csuZ/ii/g  a>!g/ts  and  suffs  of  thi  first  section  of  the  triangulation  ivest  of  Dauphin  Island  base  net 


stations.  Observed  angles, 

o  /  // 

Petit  Bois  50    49     13  76 

Point  aux  Pins  47     37     13  '21 

Dauphin  Island  West  Base     Si     33     33  "66 


Correc- 
tion. 


Grande  Batture  54  50 

Point  aux  Pins  88  51 

Dauphin  Island  West  Base  36  iS 

Grande  Batture  105  37 

Point  aux  Pins  41  14 

Petit  Bois                               •  33  08 

Grande  Batture  50  47 

Dauphiii  Island  West  Base  45  15 


Petit  Bois 

Horn  Island  East  1855 
Grande  Batture 
Petit  Bois 

Baj'ou  Ca.sotte 
Grande  Batture 
Petit  Bois 

Bayou  Casotte 

Petit  Bois 

Horn  Island  East  1855 

Bayou  Casotte 

Grande  Batture 

Horn  Island  East  1855 

East  Pascagoula 

Bayou  Casotte 

Horn  Island  East  1855 

East  Pascagoula 
Bayou  Casotte 
Petit  Bois 

East  Pascagoula 

Petit  Bois 

Horn  Island  East  1855 

Belle  Fontaine 
East  Pascagoula 
Horn  Island  East  1S55 


«3 

55 
53 
71 


57 

26 
04 
28 


01  '60 

39  '39 
19-97 

27 '05 
26-18 

05  -s? 

25 '45 
13  "69 
19 '63 
50  -66 
44-72 
26-37 


47 

103 

28 


37  ■  ^o 
09  -09 
i3'5o 


3' 
36 
52 

47     26  47  -96 

42     36  12-87 

•"^9    56  59  '65 

94    5S  25  -76 

50    31  24-37 

34     30  08  -99 


57 
107 

14 

20 

155 

3 


56 
52 
10 

42 
19 
58 


20-18 
39-62 
5'"^  73 

28  -49 
27-58 

51  '69 


37  13 

38  38  

104  07  58  -38 

38  42  55 '8 

95  12  56-0 

46  04  07  -o 


Splier-    Spher- 
ical ical 
angles,    excess. 


Log.  di.s- 
tances. 


Distances  in 
meters. 


-0-17  13 '59  0-20 

— o  -05  13-16  o  -19 

-+^0-17  33-83  0-19 

^O  -12  01  -48  O  -15 

-o'03  39 '36  0-15 

—0-36  19-61  0-15 

+0-36  27-41  0-13 

+0-03  26-21  0-13 

-|-o -89  06-76  0-12 

+0-48  25-93  0-17 

+0-53  14 '22  0-17 

+0-73  20-36  0-17 

-0-39  50-27  0-15 

— o  -69  44  -03  o  -14 

-0-23  26-14  0-15 

+  1-23  39-03  o-io 

+0  -02  09  -I  I  O  'lO 

--I  -34  12-16  o  -10 

-1-38  46-58  0-I4 

+  1-10  13-97  0-13 

+0-21  59-86  0-14 

— o  -j6  25  -60  o  -09 

+0  -71  25  -oS  o  "09 

+0  -60  09  -59  o  "09 

+0  -47  20  -65  o  -03 

+  1  'oi  40  -63  o  -04 

-ho  -09  58  -82  o  -03 

~I  TO  27  -39  O  -02 

— o  -38  27  -20  o  -02 

05-47  O  -02 

+  1-57  53-26  0-I5 

....  08-51  0-I5 

+0-30  58-68  0-15 

+  1 -I  56-9  o-i 

-f  O  -4  56  -4  O  -2 

-fO  "2  07  "2  O  -2 


4-193  605  2  15  617  27 

4-172  673  o  14  S82  -40 

4  -299  478  8  19  928  -69 

4-193  605  2  15  617  -27 

4  -281  040  2  19  100  -30 

4 '053  513  2  II  311  '32 

4  '299  478  8  19  928  -69 

4-134  862  4  13  641  -5] 

4 '053  5>3  J  II  311  '32 

4-172  673  o  14  882  -40 

4  -134  862  2  13  641  -50 

4-281  040  o  19  100-29 

4-134  862  3  13  641  -51 

4-121  942  o  13  241  -65 

4 '196  033  9  15  704-85 

4-134  862  3  13  641  -51 

4-254  684  9  17  975  -66 

3  -950  829  6  8  929  -55 

4  -121  942  o  13  241  '65 
4  -085  225  7  12  168-18 
4-254  6S4  7  17  975  -65 

4-196  033  9  15  704-85 

4  -085  225  8  12  168-18 

3  -950  S29  4  8  929  -55 

4  -085  225  8  12  168  -18 
4  -135  600  2  13  664  -70 

3  -546  295  3  3  51S-00 

4-254  684  8  17  975-65 

4  -326  S12  5  21  223  -28 
3-546  295  4  3  518-00  • 

4  •121  942  o  13  241  -65 

4-135  600  o  13  664-70 

4  -326  812  5  21  223  -28 

4-135  600  I  13  664-70 

4-337  600  5  21  757  -07 

4  -196  S38  o  15  733  96 


THE    xMAIN    TRIANGULATION. 


225 


i^ 


15 


16 


17 


iS 


19 


Rcsultiiii::;  aiii^lcs  and  f.id 

cs  of  Ihc  fir  si 

%C(iioii  ( 

/  Ike  lriani:;ulation  lucs 

I  of  Dai 

pliin   Island 

bast 

net  -continued 

Stations. 

observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
an«le». 

Spher- 
ical 
excess. 

I,og.  dis- 
tances. 

Distances  in 
meters. 

0 

/ 

// 

// 

// 

// 

Horn  Island  West 

42 

18 

49  0 

fi  -4 

50  4 

02 

4-135 

6<K) 

I 

'3 

664  -70 

East  Pascagoiila 

64 

47 

04-8 

t-o-4 

05-2 

0  -2 

4-263 

971 

9 

18 

,^64   19 

Horn  Island  East  1S55 

72 

54 

04  •() 

+-I-0 

05  'O 

0  2 

4-287 

827 

7 

'9 

401    16 

Horn  Island  West 

96 

06 

'4-3 

1  06 

N  9 

0  2 

4  -337 

6<j<) 

5 

21 

757  -"7 

Belle  Fontaine 

57 

03 

48  -2 

-^04 

47  •« 

0-2 

4  -263 

972 

4 

18 

364  -22 

Horn  Island  tCast  1S55 

26 

49 

57-0 

)  0-8 

57-8 

0   I 

3  -994 

618 

9 

9 

876  -86 

Horn  Island  West 

53 

47 

25-3 

-0-8 

24-5 

0  T 

4-196  838 

0 

15 

733  -96 

Belle  Fontaine 

95 

46 

44-0 

+07 

44  7 

0    2 

4  -287  827 

8 

19 

401  -17 

East  I'ascagoula 

30 

25 

.51   -2 

CO 

51  '2 

0    I 

3-994 

618 

7 

9 

S76  -85 

Deer  Island  i 

3S 

49 

057 

0  -Q 

057 

0    I 

3-994 

61S 

8 

9 

876  -86 

Belle  Fontaine 

95 

52 

55  ■! 

+0-4 

55-5 

0    I 

4-195 

161 

4 

'5 

673  -34 

Horn  Island  West 

45 

•7 

5S-' 

+  1  -o 

59-' 

0  •! 

4-049 

199 

0 

1 1 

199-50 

Ship  Island  1S55 

28 

14 

00  '5 

+  1-5 

02  "O 

0  -2 

3-994 

618 

8 

9 

876  -86 

Belle  Fontaine 

5' 

39 

23-2 

0  -Q 

23-2 

0    1 

4-214 

177 

2 

16 

374  -84 

Horn  Island  West 

ICX3 

06 

34-9 

+0-3 

35-2 

O'l 

4-312 

896 

4 

20 

554  ■«> 

Ship  Island  1S55 

31 

56 

3«-5 

-I  '5 

37  "o 

0    I 

4-049 

199 

0 

II 

199-50 

Deer  Island  i 

103 

49 

5'  -4 

-0-2 

51  -2 

0-2 

4-312 

896 

2 

20 

553  -99 

Belle  Fontaine 

44 

13 

31  -9 

+0-3 

32-2 

O'l 

4-169 

209  4 

14 

764-18 

vShip  Island  1S55 

60 

10 

39 'o 

—  0  •! 

3!^ '9 

0  "I 

4-195 

161 

4 

15 

673  -34 

Deer  Island  i 

65 

00 

45  7 

—  0'2 

45 '5 

02 

4-214 

177 

3 

16 

374  -85 

Horn  Island  West 

1  Trio ATr-»      1 r^'^ 

54 

T  r 

48 

36-8 

-07 

36-1 

0-2 

4  -169 

209 

5 

14 

764-19 

' 


226 


THE    EASTERN    OBUOUE    ARC. 


13.    SECOND    AND    LAST     SECTION     OF     THE     TRI ANGULATION    WEST    OF    THE     DAUPHIN 

ISLAND    BASE    NET,    MISSISSIPPI    AND    LOUISIANA,     1850-1S74. 

No.  34. 


Mississippi   City 
Pitcher  Point  2 


Point  Clear 


East  Pearl  River 
Rigolet  Light 

LOUI  SIANA 

Fort  Wood 


nrrt  ■^^¥'  Island, 


Sou-th  Point 


New  Orleans, 
St.  Patrick's 
Church 


Nine  Mile  Bayou 
envenue 

iProctor  Point  1853 
/McLrtello  Tower 


JBcryou  Pierre 
ux^oint 
Oyster  Pavou.  1855 

MISSISSIPPI 


Kilometers 


Statute  Miles 


^Caernarvon 


The  second  and  last  section  of  the  triangulation  stretches  west  from  the  Hne  Deer 
Island  I  to  vShip  Island  1855  and  reaches  the  astronomic  station  in  the  cit}'  of  New 
Orleans,  Louisiana,  a  distance  of  132  kilometers,  or  82  statute  miles.  .It  is  of  secondary 
and  somewhat  irregular  character  as  to  size  and  shape  of  its  component  parts,  yet 
posse.s.ses  sufficient  accuracy  to  render  it  u.seful  in  the  discu.ssion  of  the  geodetic  and 
astronomic  measures  of  the  southern  portion  of  the  oblique  arc. 

When  within  34  kilometers,  or  21  .statute  miles,  of  New  Orleans  the  triangles  are 
apparently  left  without  a  check,  but  here  we  can  take  advantage  of  a  well-determined 
and  independent  length  of  the  terminal  side  Martello  Tower  to  Bienvenue.  This  is 
furnished  by  its  direct  connection,  through  a  small  but  otherwise  well  conditioned  and 
adjusted  river  triangulation,  with  the  Magnolia  liase  line,  .situated  about  60  kilometers, 
or  3734^  statute  miles,  farther  down  the  Mississippi  River.*  This  base  was  measured  by 
Assistant  C.  H.  Boyd  in  January,  1872.  Its  length  is,  roughly,  3*6  kilometers,  or  2^ 
.statute  miles, t  and  the  corresponding  length  of  .side  Martello  Tower  to  Bienvenue  is 
6  233 "42  meters.  The  length  for  this  same  line,  starting  from  the  Dauphin  Island  base 
in  the  old  unadjusted  computation  of  1880,  is  6  233*02.  The  di.screpancy  was  removed 
by  dispersing  this  difference  in  the  adju,straent  between  this  side  and  the  .side  Deer 
Island  I  to  Ship  Island  1855,  at  the  .same  time  preserving  the  four  intermediate  and 
adjusted  parts,  as  explained  farther  on. 

In  this  branch  of  the  triangulation  it  was  foinid  sufhcient  to  give  the  resulting 
angles  either  from  the  .station  adju.stment  or  from  direct  measure,  as  the  case  may  be, 
to  the  nearest  tenth  of  a  second;  further,  the  special  tabulation  of  the.se  results  could  be 
dispensed  with,  since  they  are  given  in  the  presentation  of  the  triangles. 


*  See  sketch  of  tri.ingulation,  plate  No.  19,  Coast  and  Oeodetic  Survey  Report  for  1S79. 
tI<ogarithni  of  length  of  Magnolia  base,  3'ss8  o6,s  3. 


THE    MAIN    TRIANGULATION. 


I 


The  names  of  the  observens  and  dates  of  execution  of  the  triangulation  for  each 
station  are  as  follows: 

Name  of  station. 
Mi.ssis-sippi  City 

Cat  Islam!  1S52 

Cat  Island  1855 

Pitcher  Point  2 

Cat  Island  Light 

South  Point 
Bayou  Pierre 

Point  Clear 
Grand  Island  1S52 
Grand  Island  1S55 
Oyster  Bayou  1S55 

Nine  Mile  Bayou 
Malheureux  Point 
East  Pearl  River 
Rigolet  Light 

Shell  Point 

Fort  Wood 

Proctor  1S53 
Martello  Tower 

Battery  Bienvenue 
Ducros 

Saint  Patrick's  Church,  New  Orleans 

Astro.  Observatory,  Canal  and  Basin  streets, 
New  Orleans 

Caernarvon 


Observer. 

Month  and  year. 

S.  A.  Gilbert 

May,  1 85 1 

J.  E.  Hilgard 

Apr.  and  Oct., 

I'^iSS 

S.  A.  Gilbert 

May,  1 85 1 
Jan.,  1852 

J.  K.  Hilgard 

Sept.  and  Dec. 

1855 

R.  E.  Halter 

Feb.  and  May, 

'«57 

S.  A.  Gilbert 

Apr.  and  May, 

185  r 

J.  E.  Hilgard 

Oct.  and  Dec, 

'855 

S.  A.  Gilbert 

May,  1850 

J.  E.  Hilgard 

Dec,  1S55 

J.  S.  Harris  and  R.  E.  Halter 

Feb.  and  May, 

•■S57 

J.  S.  Harris,  R.  E.  Halter 
:'.nd  S.  Harris 

I'eb.  and  May, 

■857 

S.  A.  Gilbert 

Feb.,  1852 

R.  E.  Halter  and  S.  Harris 

Feb.,  1857 

S.  A.  Gilbert 

Mar.,  1S52 

S.  A.  Gilbert 

Feb.  and  Mar. 

1852 

J.  E.  Hilgard 

Maj-  and  June, 

1855 

S.  A.  Gilbert 

Dec,  1852 

J.  E.  Hilgard 

June,  1855 

S.  A.  Gilbert 

INIar.,  May,  and  Dec,  1S52 

J.  E.  Hilgard 

June  and  Aug. 

.  1855 

J.  E.  Hilgard 

June,  1855 

S.  A.  Gilbert 

June,  1852 

J.  E.  Hilgard 

May,  June,  and  Dec,  1855 

S.  Harris  and  R.  E.  Halter 

Jan.,  Mar.,  am' 

May,  1S58 

J.  E.  Hilgard 

Aug.  and  Dec. 

1S55 

S.  Harris 

Feb.  and  Mar. 

1S5S 

J.  E.  Hilgard 

June,  1855 

R.  E.  Halter 

Feb.,  1858 

S.  A.  Gilbert 

Mar.,  1853 

S.  A.  Gilbert 

INIar.,  1S53 

C.  H.  I5oyd 

INIar.,  1874 

S.  A.  Gilbert 

Mar.,  1853 

C.  H.  Boyd 

Apr.,  1873 
Mar.,  1S74 

C.  II.  Boyd 

Mar.  and  Apr., 

1S74 

S.  Harris 

Apr..  1S5S 

C.  H.  Van  Orden  and 
C.  H.  Boyd 

Mar.,  1873 

C.  H.  Boyd 

Mar..  1874 

228 


THE    EASTERN   OBLIQUE    ARC. 


That  branch  of  the  triaiigulation  which  reaches  New  Orleans  by  w'ay  of  the  Rigolets 
and  Lake  Pontchartrajn  could  not  be  utilized  in  consequence  of  a  break  in  the  survey  at 
the  eastern  end  of  the  lake;  the  oldstation  marks,  diligently  searched  for  in  1898,  have 
entirely  disappeared.  The  junction  made  via  Lake  Borgne,  as  presented  here,  is  direct 
and  the  corrections  due  to  adjustment  are  small. 

Leaving  the  line  Deer  Island  to  Ship  Lsland  1855  and  passing  over  two  triangles, 
the  first  special  adjustment  comprises  the  figure  Mississippi  City,  Pitcher  Point  2,  Cat 
Island  1852,  Cat  Island  1S55,  Cat  Island  Light,  South  Point,  and  Bayou  Pierre.  (See 
sketch,  p.  226.)  It  involves  12  condition  or  observation  equations  and  30  corrections 
to  directions  numbered  as  follows: 


At  Mississippi  City 


At  Pitcher  Point  2 


1.  Cat  Island  1852. 

2.  Cat  Island  1S55. 

3.  Cat  Island  Light. 

4.  Pitcher  Point  2. 


At  Cat  Lsland   1S55 


5.  Mississippi  City. 

6.  Cat  Island  1S52. 

7.  Cat  Island  1855. 

8.  Cat  Island  Light, 
g.  Bayou  Pierre. 

10.  South  Point. 

1 1.  Bayou  Pierre. 

12.  Cat  Island  Light. 

13.  Pitcher  Point  2. 

14.  Mississippi  City. 


At  Cat  Lsland  1852 


At  Cat  Lsland  Light 


At  Bayou  Pierre 


At  South  Point 


I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

XI 
XII 


15.  Bayou  Pierre. 

16.  Pitcher  Point  2. 

17.  Mississippi  City. 

18.  Pitcher  Point  2. 

19.  Mississippi  City. 

20.  Cat  Island  1S55. 

21.  South  Point. 

22.  Bayou  Pierre. 

23.  Pitcher  Point  2. 

24.  Cat  Island  Light. 

25.  Cat  Island  1852. 

26.  Cat  Island  1855. 

27.  South  Point. 

28.  Bayou  Pierre. 

29.  Cat  Island  Light. 

30.  Cat  Island  1855. 

Observation  equations. 

o=+o-3-(2)  +  (4)-(5)  +  (7)-(i3)  +  (i4) 
o=  +  o-4-(2)+(3)-(i2)  +  {i4)-(i9)  +  (2o) 
o=-o-9-(3)  +  (4)-(5)4  (8)-(iS)  +  (i9) 
o=  +  i-4-(i)+(4)-(5)  +  (6)-(i6)  +  (i7) 
o=-5-4-(6)  +  (9)-(r5)  +  (i6)-(23)  +  (25) 
o=+o-9~(io)  +  (i2)-(2o)  I  (21)  — (29)  +  {30) 

0=       0-0-(2l)+(22)-(24)   J    (27)-(28)  +  {29) 

o=  +  ri-(ro)  +  (ii)-{26)  +  (27)-(28)  +  (3o) 

o=+o-5-3-25(2)  +  4-5S(3)-i-33(4)-ro2(5)+3-87(7)-2-85(8)+o-i8(r8)  +  T-8,S(i9) 

—  2 '06  (20) 
o=  +  i3-6-2-85(7)4  i4-ii{8)-ir26(9)-3-34(ii)+5-i9(i2)"i-85(i3)~6-o9(i8)-t~6-o9(22) 

+5'37(24)-5-37(26) 
o=-i27  +  i -33(1) -I  •33(2)-6-09(8)+6-09(9)-i-85(i2)+3-i4(  13) -r29{  14) +0-34(15) 

1-64(16)4  I ■3o(  17) -,  3-51  (i8)-to-i8(2o) -3-69(22) -2-47(23 )+2-47( 25.) 
0= +3-8-3-34(10) +475(1 1)-  I ■4i(i2)-2-2o(2o)-t-2-48(2i)-o-28(22)-3-4i( 24) 
+  ii-56(26)-8-i5(27) 


THE    MAIN    TRIANGULATION. 


229 


Corrclaicx  atid  rrsitlling  corrections. 


C,  ==-0185 

(1)  = 

=  :  0-156 

(iij  = 

=  -0  -446 

(2I)  = 

=  — 0  -122 

Cj  =-f  0-119 

(2) 

0  -0S4 

(12) 

-0  - 1 1 7 

(22) 

— o-ioo 

C,  =  1  0  -398 

(3) 

-0-198 

(13) 

\  0  -40 1 

(23) 

—0  -948 

C4  =  -  0-064 

(4) 

-\  0-125 

(14) 

0-156 

(24) 

—0  -044 

C5  =  +"  776 

(5) 

—0  -167 

(15) 

-0-752 

(25) 

fo  -948 

Cs  =  4  c)  -088 

(6) 

-0  -84(  1 

(16) 

•  0  -726 

(26) 

—0  008 

C7  =  f  0-142 

(7) 

—0  -120 

(•7) 

1 0  '026 

(27) 

J  0-051 

Cg  =--0-313 

(S) 

—0-061 

(18) 

-0-157 

(28) 

+0-171 

C,  =+0-0177 

(9) 

+  1  -18S 

(19) 

f  0-312 

{29) 

+0  -054 

C,o  =  -|-o-ooio 

(ro) 

+0-316 

(20) 

+0  -068 

(30) 

—0  225 

C„  = +  0-0695 

C,,  =  — 0-0273 

The  second  special  fij^ure  submitted   to  adjustment  is  composed  of    the  stations 
given  below: 


( 


At  Bavou  Pierre 


At  Point  Clear 


At  Grand  Island  1852 


I 
II 
III 
IV 
V 

VI 


1.  Nine  Mile  Bayou. 

2.  Grand  Island  1852. 

3.  Grand  Island  1855. 

4.  Point  Clear. 

5.  Bayou  Pierre. 

6.  Grand  Island  1852, 

7.  Grand  Island  1855. 

8.  Point  Clear. 

9.  Bayou  Pierre. 

10.  Nine  Mile  Bavou. 


At  Grand  Island  iSi 


At  Nine  .Mile  Ba\ou 


1 1.  Point  Clear. 

1 2.  Bayou  Pierre. 

13.  Nine  Mile  Bayou. 

14    Grand  Island  1S55. 

15.  Grand  Island  1S52. 

16.  Point  Clear. 

17.  Bayou  Pierre. 


Obscrvalioii  < -qiia/ions. 

o=-  3-2-(2)  +  (4)-  (5)+  (6)-  (S)+  (9) 
0=  0-0  -(i)+(2)--  (9)  +  (io)  (I5)|-(i7) 
o="  1-3  ■(3)  +  (4)  (5)+  (7)-(xi)+(i2) 
o=-  o-2-(i)+(3)-(i2)  +  (i3)-(i4)  +  (i7) 
o=-63 -5-2 -51(0+5 -23(2) -2 -72(4)^1  •34(5)  +  !  •34(6)-i5 -28(8)^15 -28(10) -29 -69(15) 

+30-89(16)--!  -20(17) 
o=-3i  -6-2-45(1)  1-5-25(3)  -2 -80(4) -I  -23(5)  f  T  •23(7)-i2 -02(11)  --12-02(13)  -23-61(14) 

+24-73(16)-!  -12(17) 

Corre/ates  and  n:\ii //i/i"  corrections. 


c, =+0-473 

Cj=  -  o  -030 
C3=  4  o  -047 
€4  = -0-018 
C5= +0-0223 
06= +0-0103 


(I)= 

=  -"  "33 

(2) 

u  386 

(3) 

0  -on 

(4) 

'  0-430 

(5) 

'1  "563 

(6) 

'  0  -503 

(7) 

-1  0  -060 

(8) 

0-814 

(9) 

^  0  503 

(.0)  = 

•  0  -3 II 

(") 

0-171 

(12) 

-0-065 

(UO 

•  0  1116 

(■4) 

0-225 

(15) 

0632 

(16) 

■  f  944 

(•7) 

-  0087 

I 


;30 


THE    EASTERN   OBLIQUE   ARC. 


The  third  special  figure  treated   by  itself  involves  stations  Bayou   Pierre,   Grand 
Island  1S55,  Nine  Mile  Baj'ou,  Oyster  Bayou  1855,  and  Malheureux  Point. 


At  Bayon  Pierre 

At  Grand  Island  1.S55 

At  Nine  Mile  Bayou 
At  Oyster  Bayou  1855 


1.  Oj'Ster  Ba3-ou  1S55  At  Oyster  Bayou  1S55 

2.  Oyster  Ba3-ou  1S55 
•;.   3Ialheureux-  Point 


4.  jMalheureux  Point 

5.  Nine  JMile  Bayou 


At  Malheureux  Point 


I 

II 

III 

IV 

V 


6.  Malheureux  Point 

7.  Grand  Island  1S55 

8.  Bayou  Pierre 

9.  Grand  Island  1855 

10.  Oyster  Bayou  1855 

11.  Nine  Mile  Bayou 


Observation  equations. 

o=-i-i-(i)4-(2)-(7)  +  (8) 

o=-2-o-(2)-r(3)-(6)+(7)-(9)+(io) 

o=-3-9+(3)-(4)-(9)  +  (ii) 

o=-32-23-ii-o7(i)+o-64(2)-4-i3(5)-o'io(7)+4-23(S) 

o=-4 -6- 3 -15 (2) -2 -18(3) -2 -63(5) +  2  -95(6) -o -32  (7)-o -21  (9)+3 -98(10)  — 377(11) 

Correlates  and  resultitis:  corrections. 


C,  =  -i-i38 

(0  = 

=  —  2  -29 

(7)  = 

=+0-54 

€2=— 0-522 

(2) 

—0-82 

(8) 

+0-17 

€3=  + 1 -421 

(3) 

+0-62 

(9) 

-0-93 

C4  =  +o-3io 

(4) 

-I  -42 

(10) 

—0  -CI 

C5=  +  0-I29 

(5) 
(6) 

-1-62 

+0-90 

(II) 

+0-94 

The  next   quadrilateral — Grand   Island   1855,    Malheureux  Point,  Rigolet   Light, 
East  Pearl  River — is  treated  bj^  itself. 


At  Grand  Island  1855 


At  Malheureux  Point 


1.  Malheureux  Point 

2.  Rigolet  Light 

3.  East  Pearl  River 

4.  Rigolet  Light 

5.  East  Pearl  River 

6.  Grand  Island  1855 


At  Rigolet  Light 


At  East  Pearl  River 


7.  East  Pearl  River 

8.  Grand  Island  1855 

9.  Malheureux  Point 

10.  Grand  Island  1S55 

11.  Malheureux  Point 

12.  Rigolet  Light 


I 

II 
III 
IV 


OI>servatioii  equations. 

0=+  3-o-(i)+(2)-(4)  +  (6)-  (8)+  (9) 
0=+  o-4~(i)  +  (3)-(5)  +  (6)"(io)^(ii) 
o=-  r7-(4)  +  (5)-(7)  +  (9)-(ii)  +  {i2) 
o=-4r9-o-68(i)+5-99(2)-5-3i(3)-2-o4(4)+3-68(5)-i-64(6)-5-39(7)+7-5o(8)-2-ii(9) 

Correlates  and  resullin<r  corrections. 


€,  =  —0-784 
C.= +0-748 

C3=+0  -420 
C4= +0-249 


(i)=_o-i3 

(2)  4-0-71 

(3)  -0-57 

(4)  -0-I4 


(5)  =+o-59 

(6)  -0-44 

(7)  -176 

(8)  +2-65 


(9)  =  -o-89 

(10)  -0-75 

(11)  -rO-33 

(12)  +0-42 


thb:  main  triangulatiox. 


231 


Finally  the  lt;ii.t,nh  of  the  sides  Deer  Island  i  to  Ship  Island  1855  anrl  Battery 
Bienvenue  to  Martello  Touer  were  brouj^ht  into  accord  by  adjustment  of  the  inter- 
vening triangulation,  but  leaving  Ihc  preceding  adjusted  parts,  unaltered.  Tliere  were  6 
triangles,  the  sums  of  whose  angles  were  equated  to  i,Sfj^'  +  '-,  respectively,  and  the 
length  equation  constituted  the  seventh  condition  to  be  satisfied.  This  adjustment 
was  made  by  angle  corrections,  the  16  angles  being  marked  from  A  to  Q  as  follows: 

lietweeu  stations. 

vSliip  Island  1S55  ami  Mississippi  City. 
Deer  Island  1  and  Ship  Island  !<S55. 
Cat  Island  1S55  and  Mississip])i  City. 
Mississippi  City  and  Shi])  Island  1^55. 
Bayou  Pierre  and  Point  Clear. 
Pitcher  Point  2  and  Bayou  Pierre. 
vShell  Point  and  Rii^olet  I,i><ht. 
Rigolet  bight  and  Malheureux  Point. 
Shell  Point  and  Fort  Wood. 
Rigolet  Light  and  vSliell  Point. 
Proctor  Point  1S53  and  Fort  Wood. 
Fort  Wood  and  Shell  Point. 
Martello  Tower  and  Fort  Wood. 
Fort  Wood  and  Proctor  Point  1X53. 
Battery  Bienvenue  and  Fort  Wood. 
^  Fort  Wood  and  Martello  Tower. 

When  a  letter  designating  an  angle  is  inclo.sed  in  a  parenthesis,  it  designates  the 
corresponding  correction. 

In  e.stablishing  the  6  angle  equations  the  plane  angles  already  corrected  were 
employed.     Thus  we  have 

I.   !  0=  (A)  +  (B)  +  (R.) 
II.   I  0=  (C)  -r  (D)  +  (R.) 


Designa- 
tion ol' 
angles. 

.\t  stations. 

A 

Deer  Lslanil  i 

B 

Mississippi  City 

c 

Ship  Island  1855 

D 

Cat  Island  1.S55 

E 

Pitcher  Point  2 

F 

I'oint  Clear 

G 

Malheureux  Point 

H 

Shell  Point 

I 

Rigolet  Light 

K 

Fort  Wood 

L 

Shell  Point 

M 

Proctor  Point  1S53 

N 

Proctor  Point  1S53 

0 

Martello  Tower 

P 

Martello  Tower 

Q 

Battery  Bienventie 

etc.,  where  R,,  R,. 
VII. 


refer  to  the  third  angle  of  the  triangle. 


o=~32-5+o73  (A)  -2-31  (B)  m-ivSi  (C)  -0-50  (D)  -11-36  (E) 
-0.79  (H)  -4-2-88(1)  -3-69  (K)  ^o-8o  (L)  -i-So  (M) 
-4-12   (P)    -3 '92  (Q) 


-0-98   (F)  ^-3-53  (G) 
-0-99  (X)  -07S  (O) 


where  —  33 "5    is   the  discrepancy   of    length   in   the    sixth    place    of    decimals    of    the 
logarithm. 

The  corresponding  corrections  are — 


(A)  =-fo-5 

(B)  -07 

(C)  -0-6 

(D)  -0-4 


(E)  =-t-o-5 

(F)  -0-4 

(G)  :  1  -I 
(H)      -07 


(n=-t-i'3 
(K)  -1-4 
(L)  -0-5 
(M)     -0-6 


(X)=-o-4 
iO)  -0-3 
(H  -17 
IQ)     -1-6 


2^2 


THE    EASTERN    OBLIQUE    ARC. 


Resulting  angles  and  sides  of  . 


I  Mississippi  City 
Deer  Island  i 
Ship  Island  1S55 

!Cat  Island  1S55 
Mississippi  City 
Ship  Island  1S55 

I   Pitcher  Point  2 
Mississippi  City 
Cat  Island  1.S55 

f  Cat  Island  Light 

4  I    Mississippi  City 
[  Cat  Island  1855 

r  Cat  Island  Light 

5  '.    Pitcher  Point  2 
[•  Cat  Island  1S55 

f  Cat  Island  Light 

6  I    Pitcher  Point  2 
[   Mississippi  City 

I   South  Point 
Cat  Island  Light 
Cat  Island  1855 

f    Haj'ou  Pierre 
8  I    Cat  Island  Light 
[  South  Point 

IHa)'ou  Pierre 
Cat  Island  1S55 
South  Point 

f   Cat  Island  1852 

10  I    Pitcher  Point  2 

[   Mississippi  City 

I   Bayou  Pierre 
Pitcher  Point  2 
Cat  Island  1S52 

(    Bayou  Pierre 
12  •!    Pitcher  Point  2 
Cat  Island  Light 


second 

rnd  las 

'  section 

of  the  ti 

iangiila 

fion  ii'es 

t  of 

the  Dauphin 

island  l>ase  net. 

Obser\'e' 

!  angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

spher- 
ical 
exces.s. 

Log 
distances. 

Distances  in 
meters. 

0 

/ 

/  f 

// 

n 

// 

42 

21 

51  -4 

-07 

507 

0'2 

4-169 

209 

14 

764-17 

70 

44 

54  7 

+0-4 

55-1 

0-3 

4-3'5 

662 

20 

685  -3 

66 

53 

14-8 

-1  o-i 

14-9 

0  '2 

4  '304 

316 

20 

'5'   9 

76 

28 

33-5 

-0-5 

33-0 

0-3 

4 '3 '5 

662 

20 

685  -3 

54 

ID 

30  '6 

-0-3 

30-3 

0  -2 

4-236 

793 

17 

250-2 

49 

20 

56-9 

40  "5 

57  "4 

0  -2 

4-207 

942 

16 

141  -4 

64 

00 

127 

i   DM 

12  -8 

O-I 

4-207 

942 

16 

141  -4 

57 

37 

19  0 

+  0-2 

19-2 

0"2 

4-180  886 

15 

166  -5 

5^ 

22 

29-1 

-0-6 

28-5 

0  '2 

4-184 

451 

15 

291  -5 

48 

15 

01  '4 

-0-3 

t)l  T 

0  T 

4-207 

942 

16 

141  -4 

24 

39 

28  -5 

— O'l 

28  "4 

OT 

3 '955 

5i> 

9 

026  -32 

107 

05 

3"  '9 

0  •(_) 

30-9 

0'2 

4-315 

551 

20 

680  -Q 

94 

54 

55-4 

[-0  '2 

55-6 

OM 

4-180 

886 

'5 

166    5 

36 

22 

02  -3 

1  c-i 

02-4 

OT 

3  '955 

511 

9 

026-32 

48 

43 

01  -8 

1-0-5 

02-3 

(}  "1 

4  -058 

394 

1  r 

439  '2 

46 

39 

54-0 

to -5 

54-5 

0  -I 

4 -184  451 

15 

291  -5 

lOO 

22 

15-0 

+0  -1 

15  ■! 

0-2 

4-315 

55' 

20 

680  -o 

32 

57 

50  -5 

+0  -3 

50  8 

0  'I 

4  -058 

394 

11 

439-2 

79 

59 

I  2  -u 

-0-3 

n  7 

0  'I 

3  -955 

5'i 

9 

026  -32 

43 

50 

36-5 

—  0  '2 

36-3 

e)  X) 

3  -802 

717 

6 

349-17 

56 

10 

12-5 

-0-4 

12  •[ 

0  •() 

3-881 

619 

7 

614  -11 

31 

43 

28  ■() 

+  0-I 

28-1 

0  -1 

3-881 

619 

7 

614  -1 1 

82 

28 

30 '3 

0  'O 

30-3 

0  •! 

4-157 

014 

14 

355  -4 

65 

48 

02  "O 

—0  'I 

01  "9 

0  •! 

4-120 

824 

'3 

207  '6 

10 

19 

10  '9 

I  0  •  I 

I  r  'o 

0  'O 

3  '802 

717 

6 

349  •'7 

23 

53 

36-2 

-0-8 

35  '4 

0  'O 

4 '157 

012 

14 

355 '3 

■45 

47 

14  -o 

-0  "4 

'3-6 

0  'U 

4-299 

466 

19 

928  •  1 

58 

23 

12  -2 

-07 

"  '5 

0  -2 

4-184 

451 

15 

291  -5 

63 

5S 

09-4 

-0  7 

087 

0  '2 

4-207 

760 

16 

1347 

57 

38 

4' '  "3 

0  'O 

40-3 

0  •[ 

4  •  1 80 

939 

15 

168-4 

40 

28 

33  '9 

f- 1  -9 

35  ••"! 

0  -2 

4-:8o 

939 

'5 

168-4 

5'^ 

33 

52  T 

-\-  2  T. 

54  ■' 

0-3 

4  -299 

670 

19 

937  '5 

80 

57 

29 '4 

'I  '5 

30-9 

o'3 

4  -36  > 

'73 

23 

076-7 

'9 

04 

14-9 

0  'I 

4-058 

394 

1 1 

439  "2 

22 

09 

46-5 

-l-I   -2 

47  7 

0  •] 

4-120 

822 

•3 

207-5 

138 

45 

57-8 

—0  "I 

57  7 

Q-I 

4  -363 

172 

23 

076  -6 

No. 


'3 


14 


16 


17 


18 


19 


23 


24 


25 


THE 

MAIN   Tl 

^lAXGl 

JLATIO 

X. 

233 

Ititifi  ani;lcs  and  sides 

0/  the  si'coiid 

(/;/(/  last  section 

of  til e  li 

i  amenta! 

ion  Ti'est  of  the  Pauphin 

[xlan 

I  tiase  net — continued. 

Stations 

Observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

Spher- 
ical 
excess. 

I.^g.  dis- 
tances. 

Di.stance  in 
meters. 

0 

/ 

// 

// 

// 

// 

Point  Clear 

64 

54 

08  '4 

'  '3 

07-1 

0-4 

4-363 

'73 

23 

076  7 

Pitcher  Point  2 

57 

06 

43-' 

-0  -3 

42-8 

o'3 

4-330 

386 

21 

398  -6 

Bayou  Pierre 

57 

59 

12  •! 

0  -9 

I  1    2 

0-4 

4-334 

601 

21 

607  3 

Grand  Island  1S52 

84 

46 

367 

1  '  -3 

38-0 

0  -2 

4  -330 

386 

21 

398 -6 

Point  Clear 

57 

34 

03  -6 

+  I-I 

047 

f)  -2 

4  -25.S 

550 

18 

'36-4 

Bayou  Pierre 

37 

39 

17-1 

[0-8 

17-9 

0-2 

4-118 

166 

'3 

1 27  0 

Nine  Mile  Bayou 

60 

20 

44-1 

+  0-5 

44-6 

0  -2 

4  -25.^ 

550 

18 

'36  -4 

Grand  Island  1852 

79 

41 

'9-3 

-0    2 

.'9 -I 

0  -2 

4  3 '  2 

446 

20 

532  7 

Bayou  Pierre 

39 

57 

57-2 

-0  -3 

56 '9 

0  -2 

4-127 

275 

'3 

405  -3 

Grand  Island  1855 

«3 

22 

26-6 

+  0"2 

26-8 

0-2 

4  -330 

386 

21 

398  -6 

Point  Clear 

59 

3'^ 

59  •« 

4-0 -6 

60-4 

0-2 

4-269 

2S5 

18 

590  -2 

Bayou  Pierre 

36 

5S 

32  "9 

ho -5 

33 '4 

0  -2 

4112 

5>7 

12 

957-4 

Nine  Mile  Bayou 

52 

39 

39-2 

I  -o 

38  -2 

0-4 

4  -330 

3'^6 

21 

398-6 

Point  Clear 

49 

43 

oS-i 

0-3 

4-312 

446 

20 

5327 

Bayou  Pierre 

77 

37 

14 '3 

+0-5 

14-8 

0-4 

4-419 

772 

26 

288  -9 

Grand  Island  1S55 

77 

18 

47 -2 

+0-I 

47-3 

0  '2 

4  -3 1 2 

446 

20 

532  1 

Bayou  Pierre 

40 

3'"1 

41  -4 

Q-O 

41  -4 

0'2 

4-137 

CXJ7 

13 

709  0 

Nine  Mile  Bayou 

62 

02 

3 1  ■•'^ 

+  0  ■  1 

3f9 

0-2 

4-269 

286 

18 

59<^--3 

Oyster  Bayou  1855 

94 

"5 

44-8 

0  -4 

44  "4 

0-2 

4-269 

285 

iS 

590  -2 

Grand  Island  1S55 

43 

33 

07-2 

-o-S 

06-4 

01 

4-108 

621 

12 

841-7 

Bayou  Pierre 

42 

21 

07-3 

+  2-3 

09-6 

O'l 

4  -09S  85  7 

12 

556-2 

Oyster  Ba^ou  1855 

81 

20 

57 '2 

^2  -2 

59 '4 

00 

4-137 

tx)7 

•3 

709-0 

Nine  Mile  Bayou 

64 

53 

'9  9 

Q-I 

4-098 

S57 

12 

556  -2 

Grand  Island  1855 

33 

45 

40  •  1 

r-o  -8 

40-9 

CM 

3  -886 

843 

/ 

706    25 

Malheureux  Point 

56 

26 

46-2 

•  0-9 

47  ■' 

4  -09« 

857 

12 

556  -2 

Grand  Island  1855 

77 

47 

23 '5 

•  1  "5 

25-0 

4  - 1 68  0S3 

'4 

725  9 

Oyster  Bayou  1S55 

45 

45 

4S-3 

-0-4 

47-9 

4  -033 

214 

lO 

794  -8 

Malheureux  Point 

84 

22 

34  -6 

+  1-9 

36-5 

4-137 

W7 

13 

709  0 

Grand  Island  1855 

44 

01 

43  '4 

1-0-6 

44 -o 

3  '9'*^' 

100 

9 

574   i-I 

Nine  Mile  Bayou 

51 

35 

38  ■  1 

•  I  -4 

39  "5 

4  -033 

214 

IC. 

794  -8 

Malheureux  Point 

27 

55 

48-4 

;-0  -9 

49  3 

3  -886  843 

7 

706  -25 

Oyster  Bayou  1855 

35 

35 

08  '9 

:  2-5 

II  -4 

3  -98" 

ICK) 

9 

574 -U 

Nine  Mile  Bayou 

116 

28 

59  '3 

4-168  083 

14 

725  -9 

Rigolet  Light 

29 

i;. 

63  -2 

3  '5 

59  7 

4  -033 

214 

10 

794-8 

Grand  Island  1855 

52 

42 

52  '3 

■  11  -8 

53  ■ ' 

4  -245 

179 

'7 

586  -5 

Malheureux  Point 

98 

^'3 

"7  '5 

0  '3 

07  -2 

4  ■340 

165 

2 1 

■885  -9 

P'ast  Pearl  River 

55 

47 

55  -6 

■  I  -I 

567 

4  -033 

214 

10 

794  -8 

Grand  Island   1855 

72 

"4 

21   5 

0  -5 

21  -o 

4-094 

055 

12 

418 -I 

;Malhetu-eu\-  Point 

52 

<i7 

43  -3 

I  'o 

42  3 

4 -012 

962 

10 

303  "O 

234 

THE 

EA 

vSTERf 

J    OBLI 

QUE    A 

RC. 

Resulting  angles  ami  sides  of 

the  see 

^!Ul 

met  las 

'  seetioii 

of  the  li 

iaugitlatioii  west  0/  thi 

'  Dauphin 

I  si  a  J! 

d  base  n 

et — continued. 

No.                              stations. 

Observed 

angles. 

Correc- 
tion. 

Spher- 
ical 
angles. 

^t!r     Log. 

excess,         '^-t^'^-- 

Distance 
in  meters. 

0 

/ 

// 

// 

// 

// 

East  Pearl  River 
26  •'    Malheureux  Point 
Rigolet  Light 

89 

09 

45-8 

+0-9 

467 

4-245    179 

17   586-5 

45 

55 

24  '2 

+  0-I 

24-3 

4-101    598 

T2    635  -7 

44 

54 

48-3 

+07 

49 'o 

4  '094  054 

12    41S  -I 

East  Pearl  River 
27  >    Grand  Island  1855 
Rigolet  Light 

144 

57 

41  '4 

+  1   -2 

42-6 

4-340  165 

21    .S85  -9 

19 

21 

29-2 

~i  '3 

27-9 

4-101   599 

12    635  -7 

15 

40 

45-1 

+4-4 

49-5 

4  012  961 

10   303  -0 

vShell  Point 

69 

28 

43-5 

-  0  -8 

427 

4-245   179 

17    586-5 

28  >    Rigolet  Light 

Malheureux  Point 

79 

39 

ii  -4 

-0-5 

32-9 

4  -266  540 

is  473-1 

30 

51 

43  ■  + 

+  I-0 

44 '4 

3-9S3  750 

9  632  -74 

Fort  Wood 

29 

40 

097 

—  2  -I 

07  -6 

3-983  750 

9  632  74 

29  \    Rigolet  Light 

36 

II 

18 -6 

+0-6 

19-2 

4  -060  338 

II  490-5 

vShell  Point 

114 

oS 

33  7 

-0-5 

33 '2 

4  -249  405 

17  758-4 

f   Proctor  Point  1S53 

49 

28 

307 

—  I  -Q 

297 

4  -060  338 

II  490-5 

30  1    Fort  Wood 

61 

1 8 

27-9 

-0-3 

27-6 

4-122  559 

13  260-5 

I   Shell  Point 

69 

13 

02-5 

-i-O  -2 

02  7 

4-150  236 

14  133-0 

Martello  Tower 
31   >    Fort  Wood 

Proctor  Point  1853 

69 

35 

34-5 

-Oj 

34-2 

4  -150  236 

14  133  -0 

45 

3? 

02 -8 

4-031  758 

10  75S-7 

64 

53 

22-6 

4-0-4 

23-0 

4-135  271 

13  654-3 

Batter}'  Bienvenue 
32       l-'ort  Wood 

[  Martello  Tower 

95 

'9 

50  '3 

-I  -6 

487 

4-135  271 

13  654-3 

27 

02 

oS-o 

3  -794  728 

6  233-44 

57 

3« 

05  -o 

-I  7 

03-3 

4-063  829 

II  583-2 

Ducros 

45 

40 

33 'o 

0  'O 

33-0 

0  ■ 

0 

3  '794  727 

6  233  -42 

33  \    Bienvenne 

82 

GO 

03-1 

+0-I 

03-2 

0  ■ 

I 

3  -935  932 

8  628  -44 

Martello  Tower 

52 

19 

23 '9 

0  -Q 

23-9 

0  • 

0 

3  -838  615 

6  896  -27 

Caernarvon 

44 

49 

59  7 

+  1-3 

61  -o 

0  • 

I 

3  -935  932 

8  62S-44 

34       Ducros 

95 

j8 

19-8 

+  1-4 

21  -2 

0  • 

I 

4  -085  848 

12  1S5-6 

Martello  Tower 

39 

51 

367 

+  1-3 

38-0 

CO 

3-894  517 

7  843  -63 

Saint    Patrick's   Church 

(center) 

27 

1 1 

44-4 

"  0  -2 

44-2 

0  ■! 

3-894  517 

7  843  -63 

35  ■ 

Ducros 

97 

16 

17-0 

~o  -3 

167 

0  -I 

4  -231  066 

17  024  -2 

-  Caernarvon 

55 

31 

59 '6 

—0  '2 

59-4 

0  • 

I 

4  -150  739 

14  149-4 

THK    MAIN    TRIAXGULATIOX. 


235 


re 


14.    SOME    STATISTICS    oi"    THK    TKIAXOULATION. 

In  the  following  tal)le  will  bo  found  some  statistics  relatin<^  to  the  trianj.(nlati(;n. 
In  the  third  column  is  given  the  number  of  triangles  contained  in  this  discussion, 
including  those  few  triangles  of  which  but  two  angles  were  measured.      In  the  next 

column  is  given  the  mean  error  of  an  angle  derived  from  the  relation  m  —  ^/  ,  whe 

A  —  closing  error  of  a  triangle  and  u  the  number  of  triangles;  in  tlie  last  ccjhunn  is 
given  the  more  precise  measure  of  accurac>',  namel\',  the  probable  error  of  an  observed 
direction  derived    from    the  adjustment  of    the  triangulation,   given    by   the   formula: 

iVpvv] 
^^  =  o"674-/ where  z' =  the  correction   required   by  the   figure   adjustment,/  its 

weight,  usually  unity,  and  c  —  number  of  conditions  that  entered  into  the  adjustment. 


Locality  or  name. 

Kpping  base  net. 
Northea,stern  boutiilary  section. 
New     England    section,    connecting 

three  base  lines. 
Fire  Island  base  net. 
Section    connecting   the    Fire  Islanil 

and  Kent  Island  bases. 
Kent  Island  ba.se  net. 
Allegheny    .section,    to    Humpback — 

Spear.* 
First  section  .south  of  the  tran.sconti- 

nental  triangulation. 
Second,  or  North  Carolina  section. 
Third,  or  South  Carolina  section. 
Atlanta  base  net. 

Fir-st  .section  west  of  Atlanta  ba.se  net. 
Second  section  west  of  Atlanta  base  net. 
Third  .section  west  of  Atlanta  ba.se  net. 
Fourth  .section  west  of  Atlanta  base  net. 
I'ifth  and  last  section  west  of  Atlanta 

base  net. 
Dauphin  Island  base  net.f 
First  section  west  of  Dauphin   Island 

ba.se  net. 
Second     section     we.st    of     Dauphin 

Island  base  net. 

Total  number  of  trianj^les 
Weighted  mean 


State. 

Number 

of 
triangles. 

Mean 
error  of 
an  angle. 

// 

Number 
of  con- 
ditions 

satisfied. 

Probable 

error 

of  an 

observed 

direction. 

/I 

Maine. 

46 

z!rO-63 

35 

=047 

Maine. 

iS 

074 

13 

"•51 

Me.,   N.    H.,   Ma.ss.,   R.    I., 

5?, 

<'  Si 

57 

0   26 

Conn. 

Connecticut,  New  York. 

'7 

0  49 

16 

034 

N.   Y.,   N.   J.,   Penn.,   Del., 

33 

0  -se 

35 

047 

Md. 

Maryland. 

12 

0  -96 

13 

041 

INIaryland  and  \'ir<;inia. 

28 

0-94 

22 

"  35 

\'ir^inia  and  North  Carolina. 

Yirginia  and  North  Carolina. 

N.  C,  S.  C,  Ga. 

Georgia. 

Georgia  and  Alabama. 

Alabama. 

.■\labama. 

Alabama. 

.■\labama . 

.•\labania. 

.Vlabania  and  Mississippi. 

.Mabama  and  Mississippi. 


2S 


o  -SS 


24  0-41 


II 

I  j" 

13 

0  72 

35 

078 

41 

0  62 

33 

I  'OO 

29 

0  -65 

25 

0-97 

23 

079 

16 

078 

18 

0  67 

13 

077 

14 

0  '36 

28 

0  63 

30 

034 

2S 

0-6S 

28 

0  '35 

5 

051 

5 

026 

19 

078 

18 

0  53 

4S5 


461 


*  Kstiniated  for  two  quailrilalerals  beyond  line  Mount  Marshall  to  Bull 
fof  little  weight  on  account  of  the  small  extent. 


:oS2 
Run. 


o  78 


±05 1 


C.  RKvSULTiNG  GKOGRAPHIC  POvSlTIONS  OF  THK  PKIN-CIPAL  STATlONvS 
OF  THE  TRIANGULATION  BKTWF:KN  CALAIS,  MAIXIv  AND  NEW 
ORLEANS,  LOULSIANA,  BASED  UPON  THE  CLARKE  SPHEROID  OF 
1866  AND  THE  DATA  OF  THE  TRANSCONTINENTAL  TRIANGULA- 
TION. 

The  geographic  positions  in  the  following  list  are  those  used  in  this  investigation 
of  the  figure  and  size  of  the  earth.  They  conform  to  those  published  in  vSpecial  Publica- 
tion No.  4,  "The  Transcontinental  Triangulation."  These  positions,  as  well  as  those 
in  Special  Publication  No.  4,  are  not  intended  to  Ijc  used  for  geographic  purposes,  and 
do  not  conform  to  the  principal  lists  heretofore  published  for  that  purpose,  namely,  for 
Massachusetts,  in  the  Report  for  1894,  Appendix  No.  10;  Rhode  Island,  in  the  Report 
for  1885,  Appendix  No.  8;   and  Connecticut,  in  the  Report  for  1888,  Appendix  No.  8. 

On  March  13,  1901,  the  Superintendent  adopted  a  uniform  standard  for  the  whole 
United  States,  to  which  all  positions  intended  for  geographic  purposes  are  to  be  reduced 
and  which  is  to  be  known  as  the  United  States  Standard  Datum.  The  New  England 
positions  referred  to  al:)ove  are  leased  upon  the  United  States  Standard  Datum.  The 
corrections  required  to  reduce  the  po.sitions  here  published  to  the  United  States  Standard 
vary  at  different  parts  of  the  arc,  and  in  general  fall  between  the  limits  Jcp  =  +  i"'9  to 
-f  2"-i,  AX  =  —  o"'5  to  ~  o"-8,  Aa=  —  i"  to  -f-  2". 


stations. 

Latitude  and 
longitude. 

,\/.iniuth. 

Hack 

a/.imtith 

To  stations. 

I,og.  dis- 
tance. 

Distance  in 
meters. 

Ne7v  ByuH$7vick. 

0 

Chamcook 

45  07  28-347 

345 

52 

03  *6o 

165 

55 

08-78 

Prince  Regents 

Redoubt 

4-37' 

372  8 

23 

5>6-5I 

<=>7 

05  02  797 

63 

13 

17-88 

242 

57 

00  -70 

Cooper 

4  529  929   I 

33 

878-88 

Graiul  Manan 

■14 

44  51 '626 

93 

12 

51  'lo 

273 

01 

oS  -6^ 

Trescott  Kock 

4  342 

006  7 

21 

978  94 

66 

49  54 '371 

143 

23 

18-98 

323 

15 

43  ■07 

I'rince  Kegeiits 

Redoubt 

4  376 

239  0 

23 

781  -49 

St.  David 

45 

15  00 -878 

319  44 

57  74 

'39 

5' 

2'  ',« 

Chamcook 

4  262 

200  0 

iS 

289-42   ^ 

Maine. 

67 

14  03  -514 

46 

50 

37 '49 

226 

42 

28  -44 

Rye 

4  315 

000  5 

20 

653 -82 

Againeiiticiis 

4.^ 

13    22 '638 

2 

36 

55  '9-' 

1S2 

35 

23-16 

Thoni  psou 

4-S32 

776  9 

68 

041-97 

70 

41  .«'S3i 

70 

12 

55  '05 

-'49 

■f' 

!0  -39 

Uiikonoonuc 

4-890 

346  8 

77 

686-72 

Bnrkf 

44 

35  54  '036 

235 

13 

08  -22 

,55 

19 

08  -45 

Kpping  Kast  Base 

4  •13'^ 

343  6 

'3 

75"  -30 

67  5S  ?i  -319 

337 

01 

27  -04 

'57 

05 

01  -62 

Pigeon 

4  -23S 

8476 

17 

35>'96 

Calai.s  Ob.servatory 

45 

1 1  03  "778 

206 

54 

46-96 

26 

5ft 

47  '9' 

St.  David 

3-9>4 

328  3 

8 

209-72 

67 

i6  ,53 '919 

293 

06 

27-23 

1 13 

14 

51  '42 

Chamcook 

4-227 

Si6  4 

16 

897-26 

Cooper 

44 

59  '  >  '570 

35' 

53  09 -93 

171 

S'' 

io-9,>/ 

Howard 

4-603 

402  I 

40 

123-80 

67 

28  03  -393 

75  09  42 '97 

-',54 

42 

27-80 

Hnmptiack 

4-720 

S93  2 

52 

5*8-79 

Eppiiifj  Ka.st  Base 

44 

4(1  07  •84.( 

-'77 

06 

5S'49 

97 

25 

23  3 1 

Howard 

4  543 

"7  5 

34 

923-48 

f'7 

49  ,S''^'595 

10 

52 

25  -53 

100 

50 

00-47 

Pigeon 

4-3*4 

324  6 

24 

228  -59 

Epping  West  Hase 

44 

41   29 '93^ 

286 

51 

55 ' '  7 

H)6 

5^ 

21  42 

Kpping  Kast  Base 

3  940 

3M  3 

S 

-15 -^^ 

67  5*^   ^TMl 

1? 

55 

06  -50 

'95 

53 

32  -'9 

Burke 

4  -032 

670  S 

10 

7S1  -30 

238 


THE    EASTERN    OBLIQUE    ARC. 


stations. 
Afaine — contimied. 
Howa  rd 

Humpback 

Mount  Blue 

Mount  Desert 

Mount  Harris 

Mount  Independence 

Mount  Pleasant 

Pigeon 

prince     Regents    Re- 
doubt 

Ragged  Mountain 
Rye 

Sabattus 
Trescott  Rock 


Nt'iu  Htunpi/iii  t'. 
Gunstock 

Monaduock 

Mount  Washington 

Unkonoonuc 

Maasach  usetfs. 
Blue  Hill 

Copecut 

Great  Meadow 


Latitude  and 
longitude. 


44  37  44  '677 

67  23  46 '486 

44  51  48770 

68  06  3.8 -896 

44  43  39  '450 
70  20  3.1 '175 

44  21  oj'joS 

68  13  38729 

44  39  52 '920 

69  oS  55  730 

43  45  31  774 

70  ig  15 '306 


Azimuth.        Back  azimuth. 


To  statiotis. 


65  14 

114  5S 

9  16 

75  IS 

341  59 
26  19 

78  30 

115  46 

52  IS 
94  jS 

2fi  55 
72  46 


oS  -So 

25  70 

19-46 
57  '53 

1 1  '.59 

26  -58 

45 '89 
16-62 

27  '54 
42-84 

48-38 
34  '95 


244  39 

294  28 

1S9  II 
254  35 
162  10 

205  59 

257  52 

295  o- 

231  39 

273  48 

206  40 
252  03 


1 1  -.85 
1479 

24  -63 
06  -04 

16-31 
17  '53 
02  -56 
31  '34 

24-14 
19-48 

27 '15 
08  -40 


Mount  Desert 
Humpback 

Mount  Desert 
Mount  Harris 

Sabattus 
Mount  Pleasant 

Ragged  Mountain. 
Mount  Harris 

Sabattus 
Mount  Blue 

Agamenticus 
Gunstock 


43  31  02306        300  32  51-33        121  00  45-86     Agamenticus 
i9  43  23-05        219  13  02-94     Monaduock 


71 


12-299 


42  51  39-141  336  14  22-31 

72  06  31  -641  32  59  09-94 

44  16  12-057  3  39  08-74 

71   18  14-620  236  02  04-01 

42  5"^  57  ■■^45  24  06   11  -in 

71  35  20-266  72  29  09-91 


42  12  41 '933 
71  ofi  53 '495 

41  43  15-238 
7"   03  37 '477 

41  52  43 ''27 
71   13  03-129 

41  55  36-706 
70  35  28-985 


1 16  02  50 -31 
155  43  43 '52 

133  IS  12-60 
175  17  04-04 

123  44  54 '33 
192  54  33 '99 

59  44   28  -05 
126  18  32-57 


156  23  22-41  Wachusett 

212  37  15-13  Mount  Tom 

1S3  36  23-95  Gunstock 

56  42  29-47  Mount  Blue 

203  54  01  '87  Wachusett 

252  07  55-50  Monaduock 

295  31  36-62  Wachusett 

335  24  28  -28  Unkonoonuc 

313  02  35-32  Beaconpole 

355  '4  52-96  Blue  Hill 

303  35  33 '64  Beaconpole 

12  58  41  '54  Blue  Hill 

239  25  42  -09  Copecut 

305  57  29-89  Blue  Hill 


Log.  rlis-     Distance  in 
tance.  meters. 


4-863  229  o 
4-794  490  4 

4-761  268  o 
4-929  927  o 

4-S34  04S  9 
4-938  61S  6 

4  a77  280  4 
4  -909  249  6 

4  '973  438  4 
4 "977  267  I 

4-824  135  I 
4-94S  470  6 


4  -647  630  o 
4  737  944  " 

4 '365  932  I 
4-579  231  4 

4  -655  000  3 
4729  513  I 


72  984-22 
62  300-34 

57  712-25 

85  099-50 

68  241-56 

86  819-76 

75  3S4'2i 
81  142-72 

94  067 -24 
94  900-20 

66  701  -43 

88  811 -78 


44  01  34  -698 

306  12 

05 '15 

126  32 

58  -37 

Mount  Independence 

4 -699  925 

8 

50 

no  -16 

70  49  22-903 

38  06 

09-79 

217  43 

27 '36 

Gunstock 

4-855  408 

I 

71 

6x1  -66 

44  27  16-964 

159  01 

42-47 

338  52 

24-67 

Humpback 

4  '687  346 

9 

48 

679 '59 

67  53  25-321 

243  33 

55 '23 

63  54 

42-96 

Ho-ward 

4 '641  374 

5 

43 

789  '96 

44  55  09 '523 

23  21 

55  '30 

203  17 

47  74 

Trescott  Rock 

4-289  384 

2 

19 

470  -82 

67  00  41 "OIO 

loi  53 

09  -22 

281  33 

48  -83 

Cooper 

4-565  481 

2 

36  768-95 

44  12  43 '434 

84  26 

23 '93 

263  47 

37 '44 

Sabattus 

4-872  442 

9 

74 

549 '19 

69  09  06 -369 

180  16 

01  -14 

0  16 

08  -59 

Mount  Harris 

4 '701  544 

4 

50 

297-27 

45  07  22  -680 

269  30 

22  -00 

89  44 

53  "6^ 

Chamcook 

4  -429  504 

7 

26 

884 -67 

67  25  32 -890 

12  16 

1 3  -96 

192   14 

27 '44 

Cooper                    t 

4-190  727 

0 

15 

514 '11 

44  08  35  -85S 

24  31 

20-64 

204  21 

16-42 

Mount  Independence 

4 '671  377 

7 

46 

922-13 

70  04  44-734 

77  57 

07-94 

257  26 

04-67 

Mount  Pleasant 

4-785  231 

" 

60 

986  - 1 2 

44  45  30-33S 

57  50 

42  -10 

237  38 

34  -60 

Ho-svard 

4-430  277 

0 

26 

932-52 

67  06  32  -099 

131  56 

03  ■3S 

311  40 

52  '33 

Cooper 

4  -580  099 

7 

38 

027 -67 

44  38  21  -352 

244  50 

15  71 

64  56 

52-13 

Eppiug  West  Base 

.4 '137  32S 

2 

13 

■,.9-18 

68  05  41  -166 

295  35 

27  -52 

115  40 

29  --14 

Burke 

4-021  662 

3 

10 

511 '44 

4  '805  515'  8  63  902  -20 

4 '975  2S7  4  94  468-59 

4-654  798  1  45  164-59 

4-913  165  6  81  877 '7° 

4-923  24S  I  S3  ^00-79 

4  -962  91S  5  91  816-03 

4-77S  S30  2  60  093-87 

4-648  835  I  44  548-71 

4 -S49  420  1  70  700  - 1 1 

4  '973  491  2  94  078  -68 


44  425-27 
54  694 '54 

23  223  74 
37  951 '7' 

45  IS5'63 
53  643  -00 


• 

THK    MAIN 

TRIANGULATION. 

239 

stations. 

I<atitude  and 
longitude. 

Azimuth. 

Jack  azimuth 

'I'o  stations. 

IX)g.  di.H- 

Distance  in 

tancc. 

meter*. 

Massac/iusells— cont'd. 

o 

Massachusetts  North 

42 

03  04 'sSl 

2  .34  33 '83 

1H2  34  08-81 

Oreat  Meadow 

4  -2H3  145  5 

19  193  12 

Base. 

71 

12   25 -7  IS 

72  44  03-22 

252  34  16-55 

Beaconpole 

4  '324  757  7 

21  123-10 

Massachusetts  Soutli 

41 

,M  47  '907 

1 26  46  ,52  -66 

306  41  01 -58 

Beaconpole 

4-178  727  3 

15  091  -32 

Base. 

71 

iS    16-951 

207  47  09 -72 

27  5 1  04  -66 

Massachusetts  North  Base 

4 -238  707  7 

■7  326 -3"> 

* 

Thouii>son 

42 

36  39 '930 

351  21  40-40 

171   27  17-43 

Manomet 

4 -885  726  S 

76  864 -6s 

70 

43  50-053 

120  44  30-14 

300  09  30 -63 

Cnkonoonuc 

4  ■910  955  0 

81    461    (jT) 

Wachusett 

42 

29  18755 

24  17  32-42 

204  04  5S-y6 

Bald  Hill 

4  797  545  0 

62  740  07 

7' 

53  14 '835 

66  36  43 -04 

246  05  55  -97 

Mount  Tom 

4 '835  503  ' 

68  470-4! 

h'/iud,'  /shiiid. 

Beaconpole 

4' 

59  40 '450 

146  50  03  -48 

326  32  26-18 

Wachusett 

4-817  279  5 

65656-77 

7' 

27  02-094 

228  55  17-53 

49  08  47 -86 

Blue  Hill 

4 -565  581  4 

36  777  "43 

Connecticut. 

Bald  Hill  ( Fairfied  Co. ) 

41 

12  47-787 

354  16  31 -28 

174  18  35-50 

West  Hills 

4-648  135  6 

44  477  01 

73 

2S   42  -425 

53  21  43 '93 

233  14  00-54 

Round  Hill 

4  SI'  236  3 

20  475 'SS 

Bald  Hill  (Tolland Co.) 

4" 

58    23-S5I 

47  57  30 '50 

227  47   12-01 

Box  Hill 

4  459  356  2 

28  797-59 

72 

1 1  55 '844 

82  45  17-34 

262  04  10-02 

Ivy 

4  933  714  3 

85  844 -VS 

Box  Hill 

41 

47  .57  748 

47  47  iS-30 

227  27  37-22 

Sandford 

4-745  910  0 

55  707  03 

72 

27  22-205 

97  22  57  -97 

276  52  12-72 

Ivy 

4  -S&S  420  3 

64  33'  0.) 

Ivy 

41 

52  16-434 

20  ,54  57  -85 

200  44  26  -86 

Wooster 

4  79'  5'3  4 

61  S74-74 

73 

13  28-707 

533  >4  05-75 

1.53  25  02  -99 

Sandford 

4-707  138  I 

50  949  29 

Mount  Tom 

42 

14  2S-749 

308  30  oS-92 

128  48  15  -19 

Bald  Hill 

4-678  iSo  7 

47  662 -93 

72 

38  55 -874 

16  12  13 -22 

196  00  09 -S3 

Sandford 

4  955  070  ' 

90  171 -67 

Round  Hill 

41 

06  1 1  -097 

355  06  36-16 

175  07  57-15 

Harrow 

4-531  267  4 

33  9^53  -45 

73 

40  26  -520 

93  36  48-78 

273  31  24 -.58 

Buttermilk 

4-061   771  2 

II  528-46 

Sandford 

41 

27  40  743 

29  14  57-16 

208  .56  10-16 

West  Hills 

4-914  716  0 

82  170-50 

72 

57  00-074 

-4  53  48-60 

254  32  26-29 

Wooster 

4-669  171  0 

46  6S4-31 

Tashua 

41 

15  35778 

16  39  34 -41 

196  32  40-09 

West  Hills 

4712  561  3 

51  5S9-,5o 

73 

15  02-0S3 

74  53  51  '31 

254  44  .50-,s6 

Bald  Hill 

4-296  541  3 

19  794  35 

Wooster 

41 

21  01 -906 

296  42   15-07 

116  51  40  -62 

Tashua 

4-348  S36  2 

22  327-30 

73 

29  1S-SS3 

354  55  05 '52 

174  57  33 '8- 

West  Hills 

4-776  212  0 

59  732-68 

New  York. 

1 

Buttermilk 

41 

06  34 '358 

337  18  08 -70 

157  24  52  -90 

Harrow 

4  '573  62S  3 

37  465-22 

73 

48  39-626 

50  48  43 -39 

230  33  55  '67 

Weasel 

4  -61 1  542  6 

40  882-98 

Fire  Island  East  Ba.se 

40  40  01 '370 

72  59  54-96 

252  53  42-31 

Fire  Island  West  Base 

4-147  953  5 

14  058-97 

73 

03  20  -690 

185  32  47 '29 

5  .W  40  57 

Kuland 

4-296  291    I 

19  7S2-95 

Fire  Island  West  Base 

40 

37  47708 

■39  03  50 "98 

318  55  34  -92 

West  Hills 

4-454  543  0 

27  198 -38 

73 

12  52-757 

212  43  36-41 

32  50  43-00 

Kulaud 

4  452  173  4 

28  325  -23 

Harrow 

40  47  53  '430 

46  46  40-35 

226  23  41 -32 

Beacon  Hill 

4  -856  466  7 

68  622  -52 

73  38  22  '949 

78  54  41 -49 

258  26  35  -67 

Sprinsjtt'ield 

4-791  0099 

61  80304 

RuUind 

40  50  39 -695 

84  27  43  -20 

264  12  iS-67 

West  Hills 

4  522  397  > 

33  296-39 

73 

01  59-070 

158  27  26-10 

33S  18  51 -86 

'I'ashua 

4-695  S47  6 

49  641 -81 

West  Hills 

40  4S  52-117 

S4  14  38-01 

264  06  14  -93 

Ham>w 

4  -25'^  590  2 

iS  158-03 

73 

25  33-130 

146  57  23-22 

326  47  37 -59 

Round  Hill 

4-5S2  434  I 

38-232-62 

Ne-cV  Jersey. 

Beacon  Hill 

40 

22  24-457 

54  04  37 -07 

233  55  44 '04 

Disboro 

4  -381  0S6  I 

24  048-59 

74 

13  42 "595 

89  II    18-23 

268  52  02  -70 

Mount  Rose 

4  -624    192  8 

42  091 -55 

Burden 

39  31  46-807 

92  19  43  -45 

272  06  19-93 

Buck 

4  ^ro  550  7 

30  16S  -29 

75 

22  53-468 

125  42  11-79 

305  29  34 -66 

Meetinshou.se  Hill 

4-541  913  0 

34  826-82 

240 


THE   EASTERN   OBLIQUE   ARC. 


stations. 
Aeiu  Jersey — cont'd. 
Disboro 

I^ippincott 

Moinit  Holly 

Mount  Rose 


Sprinfffield 
Stony  Hill 

Weasel 

Pennsylvania. 
Bethel 


Willowgrove 


Yard 


Delaware. 


Meetinghouse  Hill 

Mat  yland. 
Finlay  * 

Hill* 

Kent    Island  North 
Base  * 

Kent    Island  South 
Base  * 


I,instid'' 


Marriott  * 


Latitude  and 
longitude. 


40  14  46  '206 

74  27  26-539 

o9  43  iS '439 

75  I s  50 -435 

40  00  06 '997 

74  47  20-003 

40  22  o]  -305 

74  43  26 '437 

39  47  51 ■9S2 
74  ,S9  36725 

40  41   20 -056 

74  21   25-.S7.S 

40  07  10 -408 

74  3-1  ,S3'452 

40  52  34-725 

74  II    12-916 

39  50  44 '1 07 

75  29  25-964 

40  15  01 -301 

74  .5.S  14 '585 

40  o.S  29  -.S20 

75  06  22 -930 

39  5S  22  -673 

75  23  14  -426 

,^9  32  24-651 

7.=;  43  ,S.5  ■7'"^4 

39  42  44 '148 

75  42  40  7^ 


.\zimuth.       Back  azimuth. 


To  stations. 


lyOg.dis-    Distance  in 
tance.         meters. 


76  31  29  "oSo 

38  53  52  767 
76  52  50  -328 

38  58  24 -429 
76  20  27  -924 

.^^  .S3  ,Si  787 
76  21   58 -789 

39  o.S  19 '591 
76  29  09 '376 

38  52  25-417 
76  .36  35724 


36  59  09-68 
120  42  48  -60 

15  13  27-12 
88  20  56 '06 

37  44  05-93 
86  35  25-41 

336  08  37-91 

52  17  5571 

73  01  33 '85 
1 20  07  49-05 

342  40  01  -47 
41  07  50-79 

53  3''  10 '91 
116  48  03-07 

280  28  06-31 
3  37  06 -77 

312  12  38-26 
345  02  04  -97 

337  47  32 '53 
52  41  13 '57 

299  41  39 '27 
.»45  47  3376 

347  17  37 '09 
31  59  46-98 

67  06  19-17 
104  07  31 -29 

5  21  32 -IS 
62  20  38-41 


39  24  25-852    354  34  26-29 


20  18  03  -46 

94  38  26-59 
1.59  55  24-59 

64    4 1     GO  'oX 

135  37  .59 '69 

^2  ,53  40-15 
141  47  26.42 

24  16  04-75 
90  M  4 7 '.58 

96  37  35 '04 
166  46  12 -26 


Maryland  Heights* 


39  20  25-561        358  43  10-54 
77  43  00  -445  34  00  56  -52 


216  54  21  -32  Stony  Hill 
300  32  27  -66  Mount  Rose 

195  10  52-12  Burden 

265  05  42-10  Meetinghouse  Hill 

217  36  13-36  Pine  Hill 

266  J 2  20-93  Yard 

156  14  09-32  Ston>'  Hill 

232  10  17-61  Newtown 

252  49  15-97  I.ippincott 

299  52  39 '94  Vard 

162  45  02  -54  Beacon  Hill 

220  53  32  -66  Mount  Rose 

233  30  10-43  Mount  Holly 
296  34  55 '1 2  Newtown 

100  49  34  -50  Harrow 

183  35  29-31  Beacon  Hill 

132  19  24-93  I.ippincott 

165  06  15  -62  Burden 

'57  52  38-39  Mount  Holly 

232  34  02 -22  Willowgrove 

■19  53  55  03  Mount  Holly 

165  51  54  -70  Pine  Hill 

167  20  26-24  Lippincott 

211  55  48-61  Bethel 

246  55  43-41  Turkey  Point 

283  57  06-28  Principio 

185  20  44  -31  Buck 

242  og  24  -37  Principio 

174  35  54 '68  Linstid 

200  12  20-76  Webb 

274  25  17  09  Peach  Grove 

339  51   27  -46  Stabler 

244  30  52-03  Marriott 

3'5  32  31  "31  T^instid 

262  44  29-64  Marriott 

321  43  41  -57  Taylor 

204  1 1  23  -97  Marriott 

270  27  37  -96  Webb 

276  27  23-21  Hill  • 

346  43  44-42  Webb 

178  43  40-38  Bull  Run 

213  42  33 '59  Mount  Marshall 


4 '245  277  5 
4-420  656  6 

4-344   465  5 
4  '532  5.S4  6 

4  '456  957  7 
4  709  403  7 

4  '477  625  9 
4-325  374  2 

4-458  328  4 
4  '589  931  4 

4  '564  49S  I 
4  '675  473  3 

4 '342  240  8 
4  '509  657  7 

4-671  752  6 
4  747  79S  8 

4 '310  393  6 
4-559  914  6 

4 '473  9S4  7 
4-298  6S5  8 

4-494  280  7 
4 '595  230  7 

4-456  145  5 
4  -221  948  9 

4-414  063  I 
4-382  796  0 

4-283  056  5 
4 '454  159  6 

4  "550  3'6  3 
4-574  261  9 

4  -4S2  609  8 
4-420  998  3 

4  •411  765  7 
4  '253  398  2 

4 '328  444  o 
4-143  529  ' 

4 '417  956  2 
4 '214  204  0 

4 '373  7'9  9 
4 '392  324  7 

4707  753  2 

4-87S    122    3 


17  590 '47 
26  342-48 

22  103-73 

34  0S4 -32 

28  63S -99 
51   21576 

30  034 -88 
21   I53'ii 

28  729-52 

38  898  -37 

36  6S5  -81 
47  366-72 

21  990-79 

32  333 '87 

46  962  -65 

55  949  '84 

20  435 '89 

36  300-67 

29  784-12 
19  892 -33 

31  209  06 

39  375 '92 

28  585-48 

16  670 'SI 

25  945 '56 

24  143 '27 

19  189-18 
28  455  -06 

35  507 '19 

37  519 '92 

30  381  '54 

26  363 -21 

25  808  -67 

17  922-48 

21  303-16 
13  916-47 

26  179-19 
16  375-86 

23  643  94 

24  678  -84 

51  021  -49 
75  530  49 


*  Stations  in  common  with  and  fixed  by  the  transcontinental  triangulation. 


THE    MAIN    TRIAXGULATION. 


241 


stations. 

Ma>y/a  lid— continued. 
Osboriies  Ruin  * 

Principio 

Pooles  Island* 

Soper* 

Stabler* 

Sugar  Loaf* 

Swan  Point* 

Taylor* 

Turkey  Point* 

Webb* 


/  'ijginiu. 


Buffalo 


Bull  Run* 


Cahas 


Clark* 


Flat  Top 


Fork* 


Humpback* 


lyOnK  Mountain 


Mount  Marshall* 


Peach  (irove* 


Rogers 


Smith  IMountain 


Latitude-  and 
longituile 

A 

ziniuth. 

Hack  aziniutli.             To  stations. 

Log.  dis- 
tances. 

J.)istancc  in 
meters. 

0     '        " 
39  27  52  796 

c 
555 

3S  26-43 

0      t        n 

175  39  06-70 

I'oolcs  Island 

4  i"!  337  0 

20  014  14 

76   16  53'430 

73  07  42-15 

252  58  25-92 

I-'inlay 

4-340  289  4 

21  892-20 

39  35  34  '552 

I 

34  34  -59 

181   34  22 -88 

Turkey  Point 

4  -203  937  0 

15  993 -26 

76  00  17  '006 

59 

II  31-99 

239  00  57  -So 

Osbornes  Ruin 

4  -443  000  9 

27  733-26 

39  17  o5-6«i 

41 

27  16-64 

221    18  51  -52 

I.instid 

4  462  716  4 

29  021  -27 

76  IS  49-954 

121 

II  55-79 

301  02  00 -38 

l-'inlay 

4  -419  418  8 

26  267-50 

39  05  09  703 

268 

49  18-14 

88  39  42-70 

Webb 

4  -376  775  7 

23  810-90 

76  57  01-286 

343  50  29-3*^ 

163  53  07  -29 

Hill 

4  337  076  I 

21  730  -82 

39  07  15-569 

43 

31   30-39 

223  22  16-17 

Peach  Grove 

4  -48.8  456  8 

30  793-34 

76  59  07  •050 

114 

01    10-52 

293  45  41 -37 

Sugar  I.oaf 

4  ,586  513  6 

58  593-45 

39  '5  42-412 

32 

29  22-28 

212  17  39-05 

Bull  Run 

4-699  551  7 

50  067  01 

77  23  37  -423 

107 

30  00-24 

2S7  17  43-59 

Maryland  Heights 

4  -465  432  7 

29  203  -35 

39  oS  2,S  -277 

15  47  5S-81 

■95  45  40-90 

Kent  Island  North  Base 

4  -286  689  I 

'9  350-36 

76  1 6  49  -060 

71 

56  57  -47 

251  49  10-42 

Linstid 

4-272  151   I 

'8  7'3-33 

38  59  46-243 

42  39  34 -28 

222  34  07 -97 

Marriott 

4  -266  49S  5 

iS  471-34 

76  27  56-483 

170 

19  43 -07 

350  >8  57-15 

Linstid 

4   018    I9S   2 

10  427  93 

39  26  56-156 

50 

19  42-97 

230  10  02  -89 

Pooles  Island 

4  -454  483  8 

28  476-32 

76  00  35  -405 

94 

21  30-60 

274  u  09-07 

Osbornes  Ruin 

4 -370  101  8 

23  447  -78 

39  05  24 '413 

39  54  36-51 

219  46  51-13 

Hill 

4-443  72'   ' 

27  779-29 

76  40  30-733 

97 

22  49-52 

277  n  05-40 

Stabler 

4-432  017  4 

27  040-67 

36  47  44 -069 

2  28 

57  42  -54 

49  14  21  -99 

Cahas 

4  -735  69.8  6 

.54  412-49 

So  2S  39-565 

253 

08  13-16 

73  41  04  -05 

Smith  Mountain 

4-928  312  3 

84  7S3-69 

38  52  51  -450 

22 

30  41  -85 

202   ig  28 -81 

Clark 

4  -^35  447  1 

6s  461 -61 

77  42  I3'I45 

75 

02  38-38 

254  43  51-26 

Mount  Marshall 

.( -652  400  4 

44  915  -93 

37  06  59  -770 

225 

4S  35  -67 

46  04  19-60 

Flat  Top 

4  -72:  (.63  5 

53  415  04 

So  00  57-165 

285 

47  27-89 

106  03  44-13 

Smith  Mountain 

4  -619  220  5 

41  61218 

38  iS  38  -975 

63 

09  16-78 

242  36  05  -03 

Humpback 

4  -945  8 19  I 

8S  271 -22 

78  00  12  -025 

117 

25  51  -89 

297  10  2S  -99 

Fork 

4  -608  326  9 

40  581 -39 

37  27  04 -683 

249 

54  24-62 

70  oS  44  -49 

Tobacct)  Row- 

4 -567  0S3  6 

36  904  -86 

79  34  5S  -92S 

291 

56  16-53 

112    14   21 -Sg 

Long  Mountain 

4  -676  543  2 

47  483-55 

38  28  42-681 

35 

52  1 1  '94 

215  34   15-71 

Humpback 

4  -S60  307  4 

72  494 -8S 

7S  24  57  -999 

66 

26  43  -47 

245  53  1S-19 

Klliott  Knob 

4 -933  S7S  S 

85877-38 

37  56  53-769 

88 

32  08  -02 

267  57  00 -So 

Bald  Knob 

4-922  915  2 

83  736-58 

7S  53  57  -777 

123  40  43-29 

303  25  22-28 

Klliott  Knob 

4  -640  543  9 

43  706-28 

37   17  25-480 

192 

40  49-96 

12  47  40  77 

Humpback 

4 -874  224  9 

74  S55-71 

79  05  10-772 

163 

09  09  -28 

343  05  20  "So 

Tobacco  Row 

4-502  SS6  7 

3"  S33-67 

38  46  31  -688 

341 

17    18 -02 

161  24  45 -90 

Clark 

4-735  SS3  3 

54  435  -64 

78  12  10-S13 

29 

26  44  -10 

209  iS  45  -18 

I'ork 

4  '5"  8 10  3 

57  827  73 

38  55  10-601 

84 

11    2 1  -So 

263  55  30-60 

Bull  Run 

4 -616  253  0 

41  32S-S2 

77  '3  47  -327 

159  34  44 '75 

339  28  32  -6g 

Sugar  Loaf 

4  "607  957  7 

40  546-91 

36  39  33  -968 

332  46  i2  -04 

153  00  20  -50 

l\Hir(.' 

4-883  517  2 

76  474  -60 

Si  32  42-378 

40 

46    10-34 

220  24  47-93 

Roan  Ilis;h  lUulT 

4-918  217  4 

S3  S35-67 

37  00  49-354 

I -8 

■3  04  -37 

358  12  27-17 

l-'lat  Top 

4  -686  522  9 

48  5S7-51 

79  33  57  -454 

234  04  31-61 

54  21  54-41 

Long  Mountain 

4  r.-o  ,VU  3 

52  521    IC 

*  Stations  in  common  with  and  fixed  bv  the  transcontinental  triangiilntion. 

4192 — No.  7 — 02 16 


24'- 


THE    EASTERN    OBLIQUE    ARC. 


stations. 

/  'irgi/na — coiitiiiuei 
Spear* 

Tobacco  Row  * 

Nortli  Carolina. 
Benii 

King 

Mount  Mitchell 


Ivatitude  and 
loiia:itude. 


Back  azinintli. 


To  stations. 


Log.  dis-    Distance  in 
tance.  meters. 


Roan  High  Bluff 

Young 

Soiitli  Carolina. 
Hogback 

Mauldin 


Pinnacle 

Wofford 

Georgia. 
Academy 

Atlanta  Middle  Base 

Atlanta    Northeast 
Base 

Atlanta  Southwest 
Base 

Blood 


Currahee 


Grassy 


3-  33 

40751 

90  43  50-62 

7845 

47 '192 

164 

25  09-04 

37  33  53 '594 

124 

40  32 -20 

79  'I 

26  704 

211 

01  07-74 

35  33 

52  -827 

220 

IS  10-43 

■^i  39 

38  '032 

257 

56  53 '55 

35  12 

25 '649 

141 

33  39 '31 

Si  i,S 

46 '057 

225 

34  50 '93 

35  45 

51  '44 

196 

27  56-26 

S2  15 

55  '02 

291 

50  44  -49 

36  23 

51  '403 

1 58 

33  32-10 

So  16 

59  '75^ 

196 

34  48 '69 

36  02 

45 '446 

216 

DO  54  -42 

81  09 

2474* 

243 

19  33 '69 

36  05 

33 '179 

273 

01  48-50 

82  oS 

44  '634 

323 

02  32-54 

35  44 

12-276 

126 

52  52-65 

80  3S 

51  -665 

204 

00  42 -26 

35  10 

10 '003 

232 

22  49-92 

82  17 

26782 

305 

44  12-69 

34  49 

16 '196 

157 

26  59-56 

82  38  05  '506 

236  56  13 '57 

34  56 

27  '015 

203 

23  41  -77 

82  24 

40-474 

267 

18  15-89 

35  01 

58  -585 

249 

39  13-79 

82  44 

30 '447 

2S8 

36  31 -38 

34  57 

30  -072 

200 

18  39-13 

Si  56 

07-174 

243 

53  46-98 

33  57 

30 '366 

82 

42  39-78 

83  59 

28  -860 

153 

06  53-34 

33  54 

19 '447 

232 

08  09-06 

.84  16 

38-136 

312 

22  32-71 

33  55 

55  '564 

126 

iS  04-86 

■84  14 

09-791 

191 

36  22-37 

33  52 

49  '53° 

232 

06  51  -76 

84  18 

5675S 

297 

51  14-29 

34  44 

20  -949 

246 

34  02-45 

S3  5fi 

13  -609 

294 

15  38-14 

33  59  33  '442 

223 

31  55-32 

85  00 

50  '358 

272 

34  29-97 

34  31 

42-855 

188 

10  26-00 

83  22 

33  706 

244 

14  58-60 

34  29 

oS-2So 

232 

01  27 -85 

84  19 

53  '408 

267 

37  13-27 

270  28  12 -oS  Tobacco  Ro%v 

344  20  08 -66  Humpback 

304  16  1615  Bald  Knob 

31  II  50-01  Humpback 

40  35  51-27  Poore 

78  32  iS  -85  Young 

321  21  34-31  Benn 

45  58  00-43  Young 

16  32  oS-Si  Roan  High  Bluff 

112  II  53-77  Benn 

338  26  34  -89  Buffalo 

16  44  24  -74  Cahas 

36  25  06  19  Buffalo 

63  50  32-14  Moore 

93  36  44  -46  Poore 

143  19  34-95  Benn 

306  34  58  00  Poore 

24  1 3  34  -64  Moore 

52  44  43-12  Benn 

125  56  27  Si  Wofford 

337  23  19-17  Pinnacle 

57  03  53  -95  Paris 

23  27  50  -87  Hogback 

87  34  37-37  Wofford 

69  54  47  -43  Hogback 

108  47  53  -70  Paris 

20  28  10 -iS  Benn 

64  15  15-08  King 

262  34  27-87  Atlanta  Norlhea.st  Base 

333  01   II  -19  Saw  nee 

52  09  31  -84  Atlanta  Northeast  Base 

132  26  55  60  Stone  Mountain 

306  10  41  -94  Sweat  Mountain 

■I  38  54  -02  Sawnee  ■ 

52  09  31  -84  Atlanta  Northeast  Base 

117  56  .54-30  Stone  Mountain 

66  55  53 '35  Rabun 

114  34  46-12  Currahee 

43  44  36-86  Pine  Log 

92  49  04  -34  Kenesaw 

8  13  02-19  Ralnin 

64  40  16-60  Mauldin 

52  14  54  33  Blood 

S7  57  55-37  Skitt 


4-577  326  2 
4 -649  283  4 

4  -849  042  s 
4-696  339  5 

4 -846  167  o 
4-971   70S  4 

4 -705  136  6 
4  -925  530  7 

4-579  630  9 
4-771  325   I 

4  -676  356  4 
4 -920  554  3 

5-013  257  o 
4-943  028  7 

4-950  523  6 
4  -S64  269  I 

4-758  644  5 
4-904  942  5 

4-858  124  o 
4 -602  019  6 

4  -405  5S6  3 
4-3S6  965  5 

4-441  543  7 
4-638  655  I 

4-641  697  5 
4  '503  290  4 

4-S55  901  2 
4  -800  210  3 

4 -358  1 17  9 

4  -538  n\  2 

3-6S3  590  2 

4 -215  64S  3 

4 -401  456  3 
4 -536  834  8 

3-970  276  I 
4 -249  470  6 

4  -802  267  7 
4-752  074  5 

4-701  967  7 
4-604  I  S3  7 

4-689  285  I 
4 -876  702  I 

4-661  044  2 
4 -748  161  8 


37  785-59 

44  594-72 

70  638-72 

49  698  -07 

70  172-51 

93  693 -2S 

50  715-02 
84    242-39 

37  986 -64 
59  064 -30 

47  463-13 
83  282-60 

103  099 -60 
87  705-88 

89  232-61 
73  159-22 

57  364-67 
80  341  -98 

72  131  -33' 

39  996-28 

25  444  -05 

24  376-17 

27  640-36 
43  516 -62 

43  822 -54 
31  863-27 

71  763-10 
63  126-29 

22  809-61 

34  540-94 

4  826-03 

16  430-41 

25  203-24 
34  421  -90 

9  33S  -48 

17  761-13 

63  426-06 
56  503  -39 

50  346-31 

40  196-08 

48  897  -33 
75  283-90 

45  818-85 
55  996-62 


^Stations  in  common  with  and  fixed  by  the  transcontinental  triangulatiou. 


THE    MAIN   TRIANGULATION. 


243 


I^atitiide  and 


Stations. 

lyHiuune  and 
longitude. 

Azimuth. 

Hack  a/iniutl 

To  stations. 

UOg.  (US-       1 

tance. 

Distance  in 
meters. 

Georgia — cotitinued. 

0     '        " 

0     ' 

0     /       // 

Gulf  Point 

M  37  29■V,2^ 

270  21 

36-61 

90  34  1 1  -56 

Johns 

4  529  537  9 

33  849-3'* 

85  28  02  •S24 

356  37  55 '63 

176  39  21  -02 

Indian 

4 -820  337  I 

66  120-65 

Johns 

34  37  20-912 

308  08 

41  '.SS 

128  24  21  -18 

Pine  Log 

4-732  129  0 

53  967-09 

85  05  54  -122 

27  40 

24-62 

207  33  .57-13 

Lavender 

4  ".576  176  5 

37685-70 

Kenesaw 

33  58  32  -066 

172  06 

>3'42 

352  04   16-70 

Pine  Log 

4  -587  666  4 

3«  696-03 

84  34  46-078 

228  28 

51  '33 

48  32  59-86 

Sweat  Mountain 

4-182  214  9 

15  213-00 

Ua  vender 

34  19  17-249 

269  51 

11  -27 

90  13  13-30 

Pine  Log 

4  '777  750  « 

59  944  70 

85  17  18-719 

325  09 

29'15 

145  18  44-08 

Games 

4  '647  387  9 

44  400  -50 

Pine  Log 

34  19  ifi-ooo 

236  55 

16.98 

57  05  38 -84 

Grassy 

4 -525  240  9 

33  515 '13 

84    3S    14  '012 

28  2  00 

14-29 

102  16  20  'I  I 

Sawnee 

4-651  920  I 

44  866 -28 

Kabun 

34  57  53 '468  ■ 

261  24 

26-47 

81  43  38-«« 

Pinnacle 

4-711  876  7 

51  50S-24 

S3  17  59  '673 

284  30 

08-34 

104  52  57-92 

Mauldin 

4 -798  278  I 

62  846  07 

Sawnee 

34  14  09-823 

150  29  47-95 

330  24  01  -28 

Grassy 

4-502  751  8 

31  S23-7S 

84  09  39-192 

233  23 

17-41 

53  38  oS-81 

Skitt 

4  -700  538  9 

50  180-95 

Skitt 

34  30  18-269 

142  52 

18-89 

322  44  .59  •4S 

nlood 

4-5'3  146  5 

32  594  -66 

83  43  20-214 

265  12 

55  '59 

85  24  41 -92 

Currahee 

4 -503  Soi  0 

31  900  76 

Stone  Mountain 

33  4S  19771 

149  23  30 '53 

329  20  30-22 

Atlanta  Northeast  Kase 

4-212  738  2 

16  320-68 

84  08  46  -239 

220  08 

00-33 

40  13   11  06 

Academy 

4  346  400  3 

22  202-42 

Sweat  Mountain 

34  03  ,S9-I38 

149  27 

55 '40 

329  21  48-91 

Pine  Log 

4-516  0.84  I 

32  815  -S9 

Alabama 

84  27  21  -883 

235   15 

57-16 

.55  25  53  -73 

Sawnee 

4-519  739  5 

33  093  '26 

Alpine 

33  24  40-292 

141  33 

51  -36 

321  23  17-60 

Cahaba 

4  -676  196  3 

47  445 '64 

86  12  27-492 

257  27 

29-92 

77  40  41  -45 

Cheehahaw 

4  '579  .566  6 

37  981  02 

Aurora 

34  08  45  -=,03 

236  06 

3'  -43 

,56  21  03  -04 

Brandon 

4  -677  999  5 

47  643-04 

86  II  01  -III 

280    12 

46-25 

100  38  16-17 

Indian 

4  -852  202  7 

71   154-56 

Pargeuier 

31  .S9  14-452 

135  47 

09  -65 

315  40  32-78 

Lovers  Leap 

4  '44^  35S  9 

2S  077  -53 

86  36  51  -350 

iSo  29 

12-15 

0  29  17-59 

Lowudesboro 

4  '497  668  4 

3'  453 '46 

Brandon 

34  23  05  -005 

224  31 

17  -22 

44  41  00-81 

Gulf  Point 

4 '573  iSS  9 

37  427-34 

85  45  13-034 

322    21 

46-56 

142  32  50 -86 

Indian 

4  -695  S37  9 

49  640-70 

Cahaba 

33  44  45-ilS 

215  23  39-56 

35  .35  07  -67 

Aurora 

4  736  436  7 

54  505  05 

86  31  33 '365 

293  18 

11  -30 

113  42  00-72 

Cheehahaw 

4 -S60  S04  4 

72  577 '90 

Cat  Island 

30  18  54-274 

316  16 

59  '55 

136  19  12-69 

Dauphin  Island  East  Base 

4-009  213  8 

10  214-42 

88  12  38-851 

22   45 

27-88 

202  44  20 -97 

Dauphin  Island  West  Base 

3  962  492  9 

9  172-61 

Cedar  Point 

30  20  42-488 

8  07 

4 '  -93 

iSS  07    13 '05 

Dauphin  Island  East  Base 

4  034  45S  5 

10  S25  -76 

88  07  17-561 

45  50 

55  '"T 

225  47  06-07 

Dauphin  Island  West  Base 

4-22S  357  0 

16  91 8 -51 

Cheeliahaw 

33  29  05-692 

154  46 

13-71 

.^,■^4  33  42-57 

.Aurora 

4-909  145  I 

Si   123-30 

85  48  31  -422 

210    19  49 '60 

30  32  36  -45 

Indian 

4  -845  763  S 

70  107-39 

Cold  Creek 

30  57  25 -027 

17S  54 

28-95 

35S  54  16-99 

Coon 

4  -507  002  9 

32  136  82 

88  05  20-666 

25S  07 

44  '44 

78  17  03-22 

Dean 

4  -468  673  0 

29  422  05 

Coon 

31   14  4S-35S 

229  07 

3S-35 

49  16  37-46 

White 

4-55*  422  2 

36  176-14 

88  05  43'8l' 

275  44 

45  'SlS 

95  5S  16 -99 

Red  Hill 

4  619  293  4 

41  619-17 

County  Hue 

31  57  50-224 

175  3S 

53  -09 

.3,55  3"*  i>'^'09 

Lovers  Leap 

4 '357  27S  3 

22  765-56 

86  48   12-714 

261  41 

54  -81 

81  47  55-63 

Bargenier 

4-257   I20  0 

iS  076-73 

Creagh 

31  36  11  -130 

232  4S 

02-18 

53  02  09-41 

Fatuma 

4 '-25  276  4 

55    122-24 

87  41  03-677 

306  32 

42-87 

126  30  37-61 

PoUanl 

4-415  967  1 

26  059-56 

Daphne 

30  36  05 -762 

114  19 

01  -13 

294   11  37-90 

Spring  Hill 

4  -4CM  704  4 

15  392 '44 

87  54   16  -946 

190  49  52-66 

10  51  41  -67 

Minette 

4-4?J  341  0 

30  '55  r? 

244 


THE    EASTERN    OBLIQUE    ARC. 


stations. 

Latitude  and 
longitude. 

Azimuth. 

Back 

azimuth 

To  stations. 

Log.  dis- 
tance. 

Distance  in 
meters. 

Alabama — continued. 

0     '        " 

0    '        " 

Dauphin    Island    Kast 

jO  14  54 '447 

165  06  03 -75 

345 

03  37-99 

St.  Elmo 

4-475 

527  2 

29  890 -09 

Base 

.?S  08  14  -813 

2S1  42  19-32 

lOI 

45  46-33 

Fort  Morgan" 

4-050 

203  4 

11 

225  '44 

Dauphin   Island  West 

^^0  14   19-561 

264  1 1   23  -52 

.84 

14  43 '35 

Dauphin  Island  East  Base 

4-027 

831  9 

10 

661 -S3 

Base 

SS  14  51-558 

273  oS  47-15 

93 

15  33  '90 

Fort  Morgan 

4  -335 

134  2 

21 

633-87 

Dean 

31  00  40-292 

131  43  27-82 

3" 

33  54  72 

Coon 

4 '594 

429  9 

39 

303-38 

87  47  15-226 

20S  52  32-11 

28 

56  27  -58 

Red  Hill 

4-397 

629  5 

24 

982-13 

Ethridge 

32  04  43-931 

245  52  52-05 

66 

00  24  -52 

Lovers  Leap 

4-387 

868  6 

24 

426  -92 

87  03  29-565 

297  50  iS -42 

117  58  24-57 

County  Line 

4 '434 

991  6 

27 

226  -49 

Fatama 

31  33  31  '091 

219  09  31 -86 

39 

15  12-97 

Ethridge 

4-427 

241  S 

26 

744 '95 

87  14  13-528 

258  52  11-33 

79 

05  56 -77 

County  Line 

4-620 

873  3 

41 

770  -85 

Fort  Morgan 

30  13  40-307 

149  07  17-14 

329 

01  23-61 

St.  Elmo 

4  560 

27S  0 

36 

331 '05 

88  01  23-757 

195  20  38-09 

15 

24  14-17 

Daphne 

4  '633 

149  6 

42 

96S -45 

Fort  Morgan,  A.st  Az. 

30  13  40-301 

93  15  36-00 

273 

oS  49-27 

Dauphin  Island  West  Base 

4  '335 

120  3 

21 

633 '17 

Station  1847 

.SS  01   23  -784 

143  59  50-69 

323 

56  52  -27 

Cedar  Point 

4  -206 

143  7 

16 

074  73 

Gunter 

34  34  04 -490 

297  43  27-43 

117 

57  40  -83 

Brandon 

4-638 

579  6 

43 

509 '05 

86  10  20 -627 

1   16  10-17 

;Si 

15  47 '32 

Aurora 

4-670 

3S9  7 

46  S15  -51 

Horn 

33  17  50-262 

135  37  34  '97 

315 

33  u  '83 

Alpine 

4 '247 

564  0 

17 

6S3 -33 

86  04  28-886 

229  51   58-12 

50 

CO  45-06 

Cheehahaw 

4 '509 

625  5 

32 

331 '47 

Indian 

34  01  47  -60S 

201   16  29 -13 

21 

21  05 -89 

Lavender 

4  '540  524  3 

34 

715 '57 

85  25  31 -412 

276    05    34  -QI 

96 

19  22-45 

Carnes 

4  -582 

375  3 

38 

227  -45 

Jamison 

32  55  54  -510 

218    27   36  -25 

38 

36  44  -49 

Kahatchee 

4  -621 

350  2 

41 

S16-74 

86  3S  21 -461 

259   07    53-40 

79 

17  10 -87 

Weogufka 

4 '432 

9"  3 

27 

096  -38 

Kahatchee 

33  13  36-299 

214  45  04-57 

34 

50  06  -42 

Alpine 

4-396  361  0 

24  909-27 

86  21  37  -002 

253  32  15 -48 

73 

41  39 '37 

Horn 

4  '443 

056  7 

27 

736  -82 

Laurel 

33  23  49'oi4 

1S7  32  11 -55 

7 

34  01  -55 

Cahaba 

4 '591 

482  6 

39  037  -55 

86  34  52-286 

267  17  39-53 

87  29  59  89 

Alpine 

4 '541 

410  I 

34 

7S6  -45 

Lovers  Leap 

32  10  07  -200 

177  27  23-26 

357 

26  43  -40 

Parker 

4-641 

191   I 

43 

771  -46 

86  49  iS-648 

240  10  22 -47 

60 

17  06-35 

Lowndesboro 

4-358 

925  0 

22 

852  -04 

Lowndesboro 

32  16  15-5S1 

146  II   13-53 

326 

03  47 '53 

Parker 

4 '591 

oSi  3 

39 

001  -50 

86  36  41  -140 

195  19  41  -96 

15 

23  28-61 

Wilder 

4-619 

619  3 

41 

650-41 

Midway 

31  43  03  -463 

137  05  ,59 '66 

316 

59  59'ii 

Fatama 

4-421 

772  3 

26 

410-24 

87  02  49-417 

220  06  02 -24 

40 

13  4476 

County  Line 

4 '553 

155  5 

35 

740  -08 

Minette 

30  52  07  -453 

112  50  33-81 

292  43  03-26 

Cold  Creek 

4-402 

402  0 

25 

258-17 

87  50  43  -649 

199  17  30-87 

19 

19  18  03 

Dean 

4  -223  609  6 

16 

734  -38 

Mount  Carniel 

32  01   14-072 

81  43  25-91 

261 

34  58-84 

Bargenier 

4-404 

518  7 

25 

381  -58 

86  20  54  -584 

138  17  37 '94 

318 

09  14  30 

Lowndesboro 

4  -570 

946  7 

37 

234  -60 

Parker 

32  33  46-821 

153  54  03-18 

333 

50  22-76 

Perry 

4  -383 

230  1 

24 

167-41 

86  50  33-110 

256  31  28-49 

76 

42  44 -26 

Wilder 

4  -526  629  6 

33 

622  -47 

Perry 

32  45  31 -igo 

236  59  07 -26 

57  09  25  -61 

Jamison 

4 '548 

055  3 

35  322  81 

86  57  21  -552 

287  41   12  -26 

107 

56  10-47 

Wilder 

4 '657 

953  4 

45 

493  -93 

Point  .\ux  Pins 

30  22  01  -836 

300  03  57  -(,5 

120 

07  05-54 

Cat  Island 

4-061 

419  I 

II 

5i9'ii 

88  18  51 -990 

335  41  32-18 

155 

43  33-50 

Dauphin  Island  West  Base 

4-193 

605  2 

15 

617-27 

Pollard 

31   27  46-614 

204  17  09-00 

24 

24  18 -I  I 

Fatama 

4717 

767  0 

52 

211  -60 

87  27  50-666 

234  23  07-18 

54 

36  13 '60 

Midway 

4-686  81S  9 

48 

620  -44 

Red  Hill 

31    12  30-412 

153  26  19-69 

333 

21  45-01 

White 

4  '493 

964  7 

31 

186-36 

87  ,39  39 '49° 

213  32  II  -So 

33 

38  20-43 

Pollard 

4  -529 

843  I 

33 

872-18 

1 

THE    MAIN 

TKIANGULATIOX. 

245 

stations. 

Latitude  and 
longitude. 

A/.imiitli.      I! 

ick  azimuth. 

To  stations. 

Log.  dis- 
tance. 

Distance  in 
meters 

A  Id  ba  ma — continued 

0     /    ■»„ 

0     /       '/ 

1 

Kowe 

34 

32 

19  -964 

264    12    11 -28 

84  24  09 -49 

Ounter 

4 "51 1  '49  9 

32  445 -'6 

Hfi 

31 

26  '930 

354  26  07  -69 

174  27  27-52 

Summit 

4 '572  1 15  2 

37 

3.34  9  > 

St.  Khno 

30  30 

32  -402 

198   15  34-06 

18  17  44-69 

S))ring  Hill 

4  -338  386  5 

21 

796-49 

1 

88 

13 

03 '031 

251  02  15-61 

71    1 1  48  -oS 

Daphne 

4 'SO'  323  3 

31 

719-28 

1 

Spring  Hill 

30  41 

44  '.SOS 

190  40  37-82 

10  42  23-26 

Cold  Creek 

4 '469  457  8 

29  475  27 

1 

88  oS 

46  '420 

236  14  48  -44 

56  24  02  'ss 

Minette 

4  539  029  5 

34 

5'/i29 

Summit 

34 

12 

13  -980 

215  20  58-80 

35  31  34-'<> 

(Sunter 

4-695  149  2 

49 

562-05 

86 

29  05  -522 

282  56  19-01 

103  06  28  -15 

Aurora 

4-454  925  I 

28 

505-27 

Weognfka 

32 

58 

39 '195 

178  54  29-13 

358  34  18  -02 

Kahatchee 

4-44'  562  5 

27 

64 '-55 

86 

21 

16  '659 

216   17  59-26 

36  27  10-16 

Horn 

4  -643  871  6 

44 

042  -46 

Wetumpka 

32 

32 

01  '458 

111   27  30-94 

291   17  49-29 

Wilder 

4  -480  740  5 

30 

251  06 

86 

II 

38  -672 

163  02  42-85 

342  57  30'I2 

Weo.gufka 

4-711  520  4 

51 

466  00 

White 

31 

27 

35  -857 

216  23  55 '91 

36  27  48  - 1 1 

Creagh 

4-295  003  9 

'9 

724-40 

87  48 

27 -684 

269  19  44  97 

89  30  30 -60 

Pollard 

4-514  017  4 

32 

660-09 

Wilder 

32  37  59 '434 

157  42  34  "34 

337  37  51  -32 

Jamison 

4-553  909  0 

35 

-50214 

86 

29 

38  754 

198  50  42  -47 

18  55  14  -50 

Weognfka 

4  -605  9S2  4 

40 

362-91 

Wilson 

34 

2.S 

OS  "140 

243  29  09-45 

63  39  07  '40 

Rowe 

4  -478  573  3 

30 

100-47 

86 

49 

03-198 

307  42  52-90 

127  54  oS-oi 

Summit 

4  -588  392  3 

38 

760-76 

Wornock 

33 

.S9 

46-272 

220  24  31  -96 

40  31  41  -84 

Summit 

4-481   194  5 

30 

282  -69 

Mississippi. 

86 

4> 

52  -2SS 

330  oS  31 -89 

150  14   16 -83 

Cahaba 

4-505  134   1 

31 

998  -r? 

Rellefontaine 

30 

20 

3"  '277 

269  35   12-7 

89  40  10  -3 

Kast  Pascagoula 

4-196  838  0 

'5 

733  -96 

88 

42 

34781 

5  21   57-4 

1 85    21    40-0 

Horn  Island  West 

3-994  61S  8 

9 

S76-86 

Bayou  Casotte 

30 

19 

42 '575 

273  40  46-49 

93  43  34 '91 

C'.rande  Batture 

3  -950  829  4 

S 

929 -.55 

88 

30 

47  -883 

8  39  12-09 

1 88  38  37  -5.S 

Horn  Island  East  1855 

4  085  225  7 

12 

I6S-1S 

Cat  Island  1852 

30 

14 

14-036 

133  46  36 'o 

3'3  43  09-2 

Pitcher  Point  2 

4-180  939 

15 

I6^  -37 

1 

89 

04 

04  -370 

192  09  47  -4 

12  10  51  '7 

Mississippi  City 

4  "207  760 

16 

134  -67 

Cat  Island  1S55 

30 

14 

13  -S64 

192  1 1  08  -4 

12  12  12-8 

Mississippi  Cit}- 

4  207  942 

16 

14  ■  43 

89 

04 

04 '655 

268  39  41 -4 

8S  45  06-2 

Ship  Island  1S55 

4-236  793 

17 

250-15 

Cat  Island  Light 

30 

13 

48-673 

170  07  52 -7 

350  07  15-7 

Pitcher  Point  2 

4 -05S  394 

11 

439 ''6 

89  09  40  -973 

265  02  .48  -3 

85  05  37-6 

Catlsland  1S55 

3-955  511 

9 

026  32 

1 

Deer  Island  i 

30 

21 

41  '040 

281    11   25-1 

101    14  ^2  -9 

Hellefontaine 

4  -049  199  0 

11 

199-51 

88 

49 

26-110 

320  00  30 -s 

140  03  40  -9 

Horn  Island  West 

4-195  161  4 

15 

673 -.U 

East  Pearl  River 


East  Pascagoula 


Grande  Batture 


Horn  Island  East  1855 


Horn  Island  West 


Mississippi  City 


Petit  Bois 


30   10 

.56-193 

290  33 

5'  '7 

110 

36 

52  -8 

Grand  Island  1-^55 

4  012 

962 

10 

302 -96 

89  31 

27-272 

346  21 

48-4 

166 

22 

43  -3 

Malheureux  Point 

4-004 

0.55 

12 

418-09 

30  20 

33  ■.593 

296  30 

53-20 

116 

31 

52  -72 

Bayou  Ca.sollc 

3  -546 

295 

3 

3 

518-00 

88  32 

45-725 

3.54  27 

13-86 

174 

27 

38  -76 

Horn  Island  East 

1855 

4-135 

600 

2 

'3 

(64-70 

30  W 

23  -846 

244  29 

,S8  -.38 

64 

33 

1 1  -.54 

Point  .\ux  Pins 

4  053 

5 '3 

2 

II 

3>'-32 

88   23 

14-320 

299  19 

59  -87 

119 

25 

13-89 

Dauphin  Island  W 

est  Base 

4-281 

040 

2 

19 

100  -30 

30   13 

i:  -goi 

223  08 

47-17 

43 

12 

09  -83 

I'.raiule  Batture 

4   196 

03>> 

9 

15 

704 "85 

88  31 

.56  -341 

278  35 

37  -43 

98 

39 

43  '74 

Petit  Bois 

4121 

942 

0 

'3 

241  -65 

30   15 

10-92S 

239  09 

04  -5 

59 

■4 

19-1 

East  Pascagoula 

4-287 

S27 

7 

19  401 -16 

88  43 

09  '3,i" 

281   27 

54  -9 

101 

33 

.V  -8 

Horn  Island  East 

1S55 

4 --^3 

971 

9 

IS 

364-10 

30  22 

46-232 

275  39 

51  '7 

95 

46 

11-4 

Deer  Island  1 

4  304 

316 

20 

151  -90 

89  01 

57-046 

318  01 

42  '5 

138 

06 

03-6 

Ship  Island  1855 

4  'o'S 

662 

10 

685-31 

30  12 

07  -389 

170  oS 

09 -S8 

3.50 

07 

25-80 

Grande  Batture 

4-1.^4 

Sfi 

2 

•3 

(v»I  -50 

88  23 

46-844 

254  05 

30-25 

74  09  59  -67 

Dauphin  Islaiul  \\ 

est  Base 

4-172 

673 

0 

14 

8S2  •411 

h6 


THE    EASTERN    OBUOUE    ARC. 


stations. 

Latitude  and 
longitude. 

Azimuth. 

Back 

azimuth 

To  stations. 

Log.  dis- 
tance. 

Distance  in 
meters. 

A  fississip/ii— continued. 

0 

0 

Pitcher  Point  2 

30 

19  54  '661 

249  45 

00-5 

69 

49 

32  -0 

Mississippi  City 

4-184  451 

15 

2gi  '53 

89 

10  54-368 

313 

45 

13-3 

133 

48 

39-9 

Cat  Island  1855 

4-1S0  886 

15 

166-52 

Point  Clear 

30 

15  47-120 

-'49 

17 

24-4 

69 

23 

46  "I 

Pitcher  Point  2 

4  '334  601 

21 

607  -32 

89 

23  30 -982 

314 

II 

31-4 

1.14 

16 

19-7 

Bayou  Pierre 

4-3.^0  386 

21 

398 -63 

Ship  Island  1S55 

30 

14  26 -509 

204 

59 

'8-5 

25 

01 

16 -3 

Deer  Island  i 

4-169  209  5 

14 

764-19 

88 

53  19-661 

265 

09 

57-4 

85 

15 

04  -s 

Horn  Island  West 

4-214  177  3 

16 

374-85 

South  Point 

30 

11   13-376 

128 

55 

i6-i 

308 

53 

24-6 

Cat  Island  Light 

3-881  619 

7 

614-11 

89  05  59  -440 

208 

54 

27-7 

28 

55 

25-5 

Cat  Island  1S55 

3-802  717 

6 

349-17 

Loiiiiiatia. 

Battery  Bienvenue 

29 

59  02-847 

219 

38 

iS-8 

39  40 

36-8 

Fort  Wood 

4  063  829 

11 

583-21 

S9 

52  51  -433 

314 

58  07 -5 

134 

59 

29-6 

Martello  Tower 

3-794  728 

6 

233  -44 

Bayou  Pierre 

30 

07  42  -355 

192 

15 

30-9 

12 

17 

03-3 

Pitcher  Point  2 

4 -.563  173 

23 

076  -66 

89 

13  57-793 

232 

44 

06-7 

52 

J9  05-1 

Cat  Island  1852 

4  -299  670 

19  937  -47 

Caernarvon 

29 

51  49-307 

177 

55 

53  -0 

357 

55 

47-7 

Ducros 

3-S94  517 

7 

843  -63 

89 

55  15-512 

222 

45 

53-9 

42 

48 

27-7 

Martello  Tower 

4  -085  S47 

12 

185-60 

Ducros 

29 

56  03-.SS0 

216 

56 

53-5 

36  58 

10-7 

Battery  Bienvenue 

3  -838  614   I 

6 

S96-27 

89  55  26  -070 

262 

37 

26-5 

82 

40 

05-7 

Martello  Tower 

3 -935  932  2 

8 

628-44 

Fort  Wood 

30 

03  52  -460 

236  oS 

50-4 

56 

13 

26  -9 

Rigolet  Light 

4-249  405 

17 

758  -45 

* 

89  48  15-553 

265  48 

58-1 

85 

52 

32-5 

Shell  Point 

4-060  338 

11 

490  -48 

Grand  Island  1852 

30 

08  49-748 

191 

44  45  -8 

1 1 

45 

36-1 

Point  Clear 

4-118  166 

13 

127-02 

89 

25   10-952 

276 

31 

23-8 

y6 

37 

01  -8 

Bayou  Pierre 

4 -258  550 

18 

136  -35 

Grand  Island  1S55 

30 

08  58  -526 

193 

49 

33  -5 

13 

50 

31  -8 

Point  Clear 

4-112  517 

12 

957  -37 

89 

25  26-S19 

277 

12 

00-3 

97 

17 

46-3 

Bayou  Pierre 

4-269  285 

18 

590-24 

Malheureux  Point 

30 

04  24  -258 

218 

30 

25-7 

38 

32 

31-7 

Grand  Island  1S55 

4-033  214 

10 

794  -79 

89 

29  37 -95S 

302 

54 

02  '2 

122 

55 

32-5 

Nine  Mile  Bayou 

3 -981    100 

9 

574-14 

Martello  Tower 

29 

56  ,39-747 

192 

37 

33 '0 

12 

38 

28-7 

Fort  Wood 

4-135  271 

13 

654  -35 

89 

50  06  -982 

262 

13 

07-3 

82 

16 

25-8 

Proctor  Point  1853 

4-031  75S 

10 

758 -66 

New  Orleans,  St.   Pat- 

-'9 

56  45-248 

275 

07 

42-1 

95 

12 

04-4 

Ducros 

4 -I, so  739  I 

14 

149-44 

rick's  Church 

90 

04   1 1  -530 

302 

19 

26-4 

122 

23 

53  -6 

Caernarvon 

4 '231  066  2 

17 

024-18 

Nine  Mile  Bayou 

30 

01  35-344 

174 

31 

12  -I 

.\S4 

30 

47-6 

Grand  Island  1S55 

4-137  007 

13 

709  -04 

89 

24  37-900 

239 

24 

32  -I 

59 

26 

.■56-1 

Oyster  Bayou  1855 

3-886  .843 

7 

706-25 

Oyster  Bayou  1855 

30 

03  42-646 

140 

47 

35-5 

320 

45 

06-7 

Grand  Island  1855 

4-098  857 

12 

556-16 

89 

20  .30-242 

2.M 

53 

19-9 

54 

56  36-7 

Bayou  Pierre 

4-108  621 

12 

841  -65 

Proctor  Point  1853 

29 

57  26 -888 

147 

09  48-9 

327 

07 

25-8 

Fort  Wood 

4-150  236 

14 

133-05 

89 

43  29-441 

196 

38 

18 -s 

16 

39 

29-7 

Shell  Point 

4 -122  559 

13 

260 -47 

Rigolet  Light 

30 

09  13-411 

255 

27 

45-4 

75 

31 

35-2 

East  Pearl  River 

4-101  598 

12 

635  -66 

89 

39  04-455 

300 

22 

34-6 

120 

27 

18-8 

Malheureux  Point 

4-245  179 

17 

586  -48 

Shell  Point 

30 

04   19-492 

200 

01 

05-8 

20 

02 

07  -6 

Rigolet  Light 

3-983  750 

9 

632  -74 

89 

41  07-675 

269 

29 

48-7 

89  35  34 '3 

Malheureux  Point 

4-266  540 

18 

473-11 

THE   MAIN   TRI ANGULATION.  247 


D.  ADDITIONAL  CxEOGRAPHIC  POvSlTIONS  OF  ASTRONOMIC  STATIONS 
FOR  WHICH  TRIANGLES  ARE  NOT  GIVEN  IN  THIS  PAPER  AND 
WHICH  WERE  DERIVED  DIFFERENTIALLY. 

•Stations. 

Maine. 

Banj^or  , 

Cape  Small 

Farmington 

Isles  of  Shoals,  astronomic  latitude  station 

JMassac/im^ct/s. 

Cambridge,  Cloverden  Observatory 
Cambridge,  Harvard  Observatory 
Indian 
Sbootflying 

Rhode  Island. 
Spencer 

New  York. 

New  York,  Rutherford  Observatory 

Dehi'cuare. 

Cape  Henlopen  Light-House,  astronomic  azimuth  station  * 
Dover,  astronomic  latitude  station 
Dover,  astronomic  longitude  station 

Rlaryland. 

Rockville,  astronomic  latitude  station'    , 

District  of  Cotumbia. 
Causten 

Georgetown  University  Observatory 

Seaton 

United  States  Coast  and  Geodetic  Survey  Office,  transit  in  yard 

United  States  Naval  Observatory,  old  site,  dome 

United  States  Naval  Observatory,  Georgetown  Heights,  center  of 

clock  room 

Viri^inia. 

Charlottesville,  McCormick  Observatory 
Elliott  Knob,  astronomic  azimuth  station* 
Strasburg,  astronomic  latitude  station 
Strasburg,  astronomic  longitude  station 

North  Carolina. 

Statesville,  astronomic  longituile  station  35     46     54  '34  Sci     5;,     40  44 

*  Stations  in  common  with  and  fixed  by  the  transcoutiueutal  triaugulatiou. 


I.atitiule. 

Longitude. 

0 

/ 

„ 

0 

/ 

// 

44 

48 

14-19 

68 

47 

01  -20 

43 

46 

41  -24 

69 

50 

45  20 

44 

40 

2078 

70 

09 

18-40 

42 

59 

12-87 

70 

36 

51    19 

42 

22 

44-28 

71 

07 

18-46 

42 

22 

51-48 

71 

07 

44  74 

41 

25 

44  75 

70 

40 

41  54 

41 

41 

"5  '34 

70 

2C) 

50  59 

41 

40 

41  -25 

7' 

29 

41   52 

40 

43 

49 '37 

73 

59 

■5  'IS 

3S 

46 

39  '42 

75 

05 

03-52 

39 

09 

18-59 

75 

31 

24  56 

39 

09 

18-59 

75 

3' 

2a -51 

39 

05 

09  -oS 

77 

09 

37-20 

3S 

55 

33 -'6 

77 

04 

24-37 

3S 

54 

27  -Si 

77 

04 

39-61 

3S 

53 

26  -82 

77 

00 

00 -ID 

3>'^ 

53 

10  -Ql 

77 

00 

32  -71 

3S 

53 

40-12 

77 

03 

06-68 

38 

55 

14  -89 

77 

04 

l>2  -So 

38 

01 

55  91 

78 

31 

21  -15 

38 

09 

57  '22 

79 

iS 

5'  -84 

38 

59 

27  -Si 

78 

21 

39  -74 

38 

59 

27  -S2 

78 

21 

39  -54 

2^8 


THE    EASTERN    OBUOUE    ARC. 


Atlanta,  astronomic  station 


Stations. 
Georgia. 

A/aha  ma. 


Lower  Peach  Tree,  astronomic  station 
Mobile,  astronomic  station 
Montgomery,  astronomic  station 

Louisiana, 

New  Orleans,  astronomic  station  of  1S5S 

New  Orleans,  astronomic  station  of  1880  and  1895 


I,atitude. 
o         /  // 

33     44    56-10 

31  50    -iS'si 
30    41     28  -91 

32  22     37  -37 


29     57     '■'^■05 
29     56     51  ■51 


Longitude. 


o         /  // 


84      23      19-41 


87  32     43  ■37 

88  02     33-83 
86     18    00  '92 


90    04     25  -14 
90    04     12  'iS 


E.    ADDITIONAL    GEODETIC    AZIMUTHS    COMPUTED    DIRECTLY    FROM 
THE    GIVEN    POSITIONS    OF  THE  TWO   STATIONS. 


Cape  Small 


stations. 

Maine, 
il/nssar/niseiis. 


Cambridge,  Harvard  Observatory,  dome 

Indian 

Shootfiying 

Spencer 

District  of  Columbia. 
Causten 
Seaton 


Azimuth. 

Back 

azitnuth. 

To  stations. 

0 

/ 

// 

0 

/ 

// 

155 

18 

59 '9 

335 

09 

17-1 

Sabattus 

356 

25 

25-1 

176 

25 

59 '5 

Blue  Hill- 

135 

36 

02  '6 

315 

20 

49 '5 

Copecut 

143 

03 

19-5 

322 

53 

33 '9 

Manomet 

1S5 

57 

36-5 

5 

59 

22-8 

Beaconpole 

210 

54 

38-3 

30 

59 

17-2 

Soper 

265 

32 

42-33 

85 

37 

12  -16 

Hill 

I 


I 


PART     III 


THE  ASTRONOMIC  MEASURES. 


249 


111.  THE  ASTRONOMIC  MEASURES. 


A.   RESULTS  FOR  LATITUDE  AT  THE  ASTRONOMIC  STATIONS  OF  THE 

OBLIQUE  ARC. 

I .    GENEKAI,   STATEMENT. 

The  area  covered  by  the  triaiigulation  extending  from  Maine  to  Louisiana  i.s  well 
st:pplied  with  astronomic  latitudes,  determined  by  the  Horrebow-Talcott  method.  The 
number  of  stations  is  71,  irregularly  distributed  over  the  arc,  as  maybe  .seen  in  the 
general  .sketch*  of  the  location  of  the  astronomic  stations.  In  the  northeastern  half  of 
the  arc  there  are  twice  as  many  stations  as  in  the  other  half.  In  some  localities  the 
stations  are  closely  clvLstered,  as  in  latitudes  38°  45'  to  40°,  and  in  latitudes  44°  to  45°, 
but  upon  the  whole  a  satisfactory  number  of  fairly  well  distributed  stations  are  avail- 
able for  the  .study  of  the  local  and  regional  deflections  of  the  vertical. 

At  nearly  all  the  stations  the  latitude  was  determined  with  a  zenith  telescope.  At 
iour  stations  the  determination  depends  entirely  upon  ob.servations  made  with  Air3''s 
Zenith  Sector,  f  At  two  stations  both  the  above  instruments  were  u.sed,  and  at  one  of 
these  a  tran.sit  in  the  prime  vertical  was  also  used.  At  a  few  stations  ()l)ser\-ations 
were  made  with  other  in.struments,  as  stated  in  the  abstracts  of  results.  The  results 
for  latitude  are  here  presented  in  the  form  used  in  the  di.scu.s.sion  of  the  arc  of  the  par- 
allel, but  for  those  stations  which  are  in  common  with  that  arc  the  final  \-alues  alone  are 
given.  What  has  i)een  said  respecting  instruments,  observations,  and  method  of  reduc- 
tion of  latitudes  in  the  publication  of  the  arc  of  the  parallel  applies  equally  well  to  the 
present  publication,  and  that  publication  should  be  consulted  for  further  details. 

The  ob-servations  used  extend  over  the  interval  between  the  years  1S46  and  1S9S. 
The  observations  made  before  that  time  have  been  .superseded  by  the  introduction  of 
new  measures,  using  more  refined  methods  and  .superior  instruments.  Some  results  at 
the  Harvard  College  Ob.servatory  and  the  old  Naval  Observatory  at  Washington  are 
incorporated  in  the  table  of  results.  The  reduction  of  the  observations  for  latitude  was 
examined  with  a  view  of  improving  the  mean  star  places,  and  in  those  cases  where  the 
residual,  or  difference  of  result  from  any  pair  of  .stars  from  the  indiscriminate  mean  of 
all,  was  greater  than  3)^  times  the  probalile  error  of  the  result  from  that  pair,  the  mean 
places  of  these  .stars  were  recomputed. 


*  See  Map  B  in  pocket. 

t  Kor  di.scn.ssion  of  tlie  result.-:  obtained  by  ii.sing  tliis  in.strnnient,  see  .Special  Pulilication  No.  4.    "The  Transconti- 
nental Triangulation,"  XTnited  States  Coast  andVleodetic  Survey,  Wa-sliington.  II.  C,  191x1. 

■251 


252  THE    EASTERN    OBLIQUE    ARC. 

The  method  of  determining  mean  places  of  stars  was  to  abstract  from  all  available 
catalogues  the  north  polar  distances  and  to  appl>-  to  them  such  systematic  corrections  as 
were  known  to  attach  to  the  catalogues  (principally  determined  by  the  researches  of 
Professor  Lewis  Boss ) .  These  north  polar  distances  were  next  reduced  to  a  common 
epoch,  usuall}'  the  3"ear  1890,  using  the  given  precessional  values  and  approximate 
values  for  the  proper  motion,  and  applying  relative  weights  conformable  to  a  well- 
proportioned  system,  embracing  the  catalogues  in  general.  Finally  the  most  probable 
corrections  to  the  assumed  north  polar  distances  and  proper  motions  were  derived  b}' 
application  of  the  method  of  least  squares;  the  probable  errors  of  these  quantities 
likewise  became  known.  For  convenience  of  reference  the  star  numbers  given  in  the 
abstracts  are  tho.se  of  the  British  As.sociation  Catalogue;  when  not  contained  therein, 
the  number  in  parenthesis  (  )  refers  to  the  Greenwich  Ten  Year  Catalogue  of  1880;  a 
number  in  brackets  [  ]  refers  to  the  Coast  Survey  Catalogue  given  in  Appendix  No.  7 
of  the  Report  for  1876;  an  asterisk  attached  to  any  star  number  directs  attention  to  the 
fact  that  the  star  is  also  used  in  another  pair  or  pairs  at  that  .station.  The  observed 
component  of  a  close  double  star  is  identified  by  the  subscript  letters  P,  F,  and  M, 
meaning  preceding,  following,  or  mean,  respectively. 

Referring  to  the  abstracts  of  results  at  the  several  stations  the  column  headed 
"Adopted  seconds  of  mean  N.  P.  D."  contains  the  .seconds  of  the  star's  mean 
north  polar  distance  for  the  beginning  of  the  year  of  observation,  as  adopted  in  the 
latitude  computation;  the  column  headed  ;/'  gives  the  number  of  observations  made 
upon  the  pair;  the  colunni  headed  zc  gives  the  relative  weight  assigned  to  the  result 
from  the  pair;  the  last  column,  headed  z',  exhibits  the  residual  of  the  result  from  each 
pair  from  the  weighted  mean  of  all  the  pairs. 

The  probable  errors  and  relative  weights  as  given  in  the  ab-stracts  were  determined 
as  follows: 

Let  ;?  =  the  total  number  of  observations  at  a  station  and  7/'=  the  number  upon 
any  pair,  also  />  =  the  number  of  pairs,  and  ^  =  the  difference  of  each  individual 
result  from  the  mean  result  from  //uj/  pair,  then  the  probable  error  of  a  single 
ob.servation  for  latitude  is  given  by 

^3  ^  o"455  ^^' 
n  — p 

For  the  determination  of  relative  weights  zt-  we  need  e.^  or  the  value  of  the  prob- 
able error  of  the  mean  of  two  declinations  of  a  pair;  this  may  be  obtained  either  from 
the  catalogue  mean  places  or  more  directl}-  from  the  latitude  observations  themselves. 

The  probable  error  c   of  a  mean  result  from  any  pair  is  given  by  c^  ~  ~~- '-,  where 

the  vs  ari.se  both  from  errors  of  ob.servation  and  errors  of  declination,  and  are  found  by 
subtracting  the  particular  values  q)^,  <^,,  <^^,  .  .  .  ,  of  which  there  are  />  in  lunnber 
from  q)  or  the  mean  latitude  of  all. 

The  probable  errors  e^^,  e^,  etc.  of  the  latitudes  <^^,  </>,,  etc.  are  given  by: 

^^,  =  ^'t.  +  ^-  <^\„  =  e^-^  +  —     etc . , 

where   ^^,  ^r',  —  f' and  f°=-     — H- —  4-      .      .     .  ;  hence  the  weights  w  become: 


THE   ASTRONOMIC   MEASURES. 


253 


tu. 


^(^.<)"' 


w 


.=  (... +  Q-       e,c. 


There  are  exceptional  cases  in  which  these  expressions  do  not  apph'.  When  a  north 
or  south  star  is  connected  after  reversal  of  instrument,  with  two  south  or  two  north 
stars,  the  weight  assigned  to  each  of  the  two  pairs  or  doublets  so  formed  is  two-thirds  of 
that  given  by  the  general  expression,  and  in  case  of  triplets  the  weight  is  but  one-half. 
Several  stars  observed  on  one  side  of  the  zenith  maj'  occur  with  several  stars  observed 
on  the  opposite  side;  in  such  a  case  the  combination  may  be  broken  up  into  ordinary 
pairs  or  into  doublets  or  triplets  and  the  weights  determined  as  indicated  above.  When  a 
single  or  close  zenith  .star  is  ob.served  with  instrument  direct  and  instrument  reversed 

the  expres.sion  for  the  weight  becomes  7u—{  ■ 


2C' 


+  ~ 


J 


Two  values  can  be  obtained  for   e".^ ,  one  from  the  star  catalogues 


2^ 


,  where  the 


summation  extends  over  the  two  stars  of  the  group,  and  the  other  from  the  latitude 
observations   e^ 

The  resulting  latitude  t  is  given  bv 


-4°,  and  the  larger  of  the  two  values  was  used. 


(p=- 


and  its  probable  error  by 


(P.+  -     .     .     • 

cC'^-\-ca^+.      .      .      . 

2.  DETAILS  AT  .STATIONS. 

I.  Ca/ois,  Maine. — G.  \V.  Dean.     Zenith  telescope  No.  4.     September  2  to  29,  1S57.     One  division 
of  level  =  I '''00.     One  turn  of  micrometer  =  43"'64. 


Pairs 

of  stars. 

.Adopted  seconds  of 
mean  N.  P.  D. 

h' 

TV 

Latitude. 

// 

// 

0      /         // 

// 

6  350 

*6 

365 

30-60 

48 -27 

5 

3 

45    11    10-09 

—  0   69 

*6  365 

6 

372 

4S-27 

13  '37 

5 

3 

10-30 

-  0  -90 

6  394 

6 

419 

09-46 

03  '35 

5 

5 

09  -23 

+  0-17 

6  475 

6 

520 

25 '14 

57 '12 

I 

2 

09  -70 

-0-30 

6  4S0 

-6 

496 

45 '94 

25  -32 

5 

3 

09-25 

-  0-15 

6  491 

*6 

496 

14  '34 

25 '32 

5 

3 

09  -00 

—  0-40 

6  547 

6 

555 

35  -SS 

13-12 

3 

4 

09  -26 

+  o"i4 

6  566 

6 

593 

55 '50 

17 -87 

4 

4 

09-S9 

-0-49 

6  629 

6 

690 

oS-47 

16-56 

2 

3 

08  -36 

-  I  -04 

*6  635 

6 

65  > 

19 '32 

40-97 

5 

3 

10-27 

-0-87 

*6  635 

6 

667 

19-32 

58  -60 

5 

3 

10-09 

—0  -69 

6  6S7 

6 

711 

09  '55 

50  -24 

4 

4 

10  -21 

— o-Si 

6  721 

6 

745 

43  '40 

35  79 

3 

4 

10-96 

-1-56 

6  717 

*6 

769 

so  -9S 

04-90 

3 

2 

08-54 

-fo-S6 

6  741 

*6 

769 

41  -70 

04-90 

4 

3 

08-30 

-fl     lO 

t  The  details  of  the  method  of  making  and  reducing  astronomic  observations  used  in  the  Coast  and  Geodetic 
Sur\-ey  are  published  in  the  Report  for  1^97-98.  .Vppendix  No.  7,  "Determination  of  Time,  Longitude,  Ijititude. 
and  Azimuth." 


254 


THE    EASTERN    OBLIQUE    ARC. 


I.   Calais,  Maine — continuei 


Pairs  o 

f  stars. 

6  763 

*6  S17 

6  764 

*6  .S17 

6  784 

6  S47 

6  S51 

*6  924 

*6  924 

6  99S 

6  944 

6  994 

7  060 

7  131 

7  062 

*7  119 

7  091 

*7   119 

7  176 

7   194 

7  204 

7  215 

7  ^41 

7  268 

7  277 

*7  294 

*7  294 

7  3S3 

7  301 

^^7  333 

*7  333 

7  345 

7  365 

7  3«5 

7  39''' 

7  4S8 

7  465 

7  494 

7  521 

7  560 

*7  623 

7  699 

*7  623 

*7  707 

7  693 

-7  707 

*7  71S 

7  72r 

*7  71S 

7  731 

*7  753 

7  778 

*7  753 

7  7«2 

7  766 

*7  79« 

*7  79'S 

7  S29 

7  S15 

7  880 

7  S45 

7  906 

7  923 

7'  973 

7  972 

7  999 

8  023 

"8  082 

*8  028 

8  059 

*8  028 

*8  082 

8  114 

8  171 

8  188 

*8  211 

*8  211 

8  268 

51 

60 

92 

*I5S 

*I5S 

169 

Adopted  seconds  of 
mean  N,  P.  D. 

n' 

70 

Latitude. 

V 

// 

// 

0, 

/         // 

// 

iS  -35 

43-16 

4 

3         45 

11    10-33 

-0-93 

45 '64 

43-16 

5 

3 

09  -90 

—0-50 

08  "90 

00  -62 

2 

3 

07-84 

+  1-56 

39  '^0 

17-30 

4 

3 

08-54 

+0-86 

17  '30 

43-00 

I 

I 

07-45 

+ 1  -95 

44  "21 

27  -oo 

2 

3 

09-63 

-0-23 

59 '69 

28  -60 

4 

4 

08  -48 

,    +0-92 

2 1  70 

09-75 

6 

3 

08-99 

+0-41 

38-1. 

09-75 

6 

3 

09-65 

-0-25 

38  -28 

00  -80 

5 

5 

08-98 

+0  -42 

47-69 

55  -60 

4 

4 

09  -40 

0  -00 

39  '50 

43  -00 

5 

5 

09  -40 

0  -00 

53-13 

30  76 

3 

2 

08  -86 

+0-54 

30-76 

41  -63 

3 

2 

oS  -67 

+0-73 

08  '22 

27-17 

6 

3 

09-94 

—0-54 

27-17 

28  -33 

6 

3 

09-92 

—0-52 

10  '66 

47-27 

6 

5 

10  -30 

—0  -90 

10-65 

09-62 

3 

4 

08-63 

+0-77 

54  -87 

47-30 

6 

5 

09-18 

-t-O-22 

37-40 

42  -03 

7 

5 

10  -43 

-I  -03 

26  '31 

30  -74 

6 

3 

09-54 

-0-14 

26  -31 

40  -53 

3 

2 

10  -03 

— 0  -63 

44-43 

40  -53 

4 

3 

09-47 

-0  -07 

22-51 

28-68 

3 

2 

10  -I  I 

-0-71 

22  -51 

1 8 -35 

2 

2 

09  -98 

-0  -58 

56  -34 

06  -19 

4 

3 

09-13 

+0-27 

56-34 

31  -74 

4 

3 

09-32 

+0  -08 

54-51 

18  -40 

6 

3 

09  -63 

-0-23 

18  -40 

53-93 

4 

3 

10  -16 

—  0  -76 

10  -98 

16  -71 

4 

4 

oS-62 

+  0-78 

26  -22 

09-07 

5 

5 

09  -86 

-0-46 

31  '43 

46-55 

4 

4 

07-89 

+  1  -51 

48  -35 

44-54 

4 

4 

oS-70 

+  0-70 

29-46 

27  -80 

4 

3 

08  -56 

-Ho -84 

37  -47 

57  -50 

5 

3 

09-25 

+0-15 

37-47 

27  -80 

5 

2 

09  ■  1 8 

+0  -22 

56-00 

28  -62 

5 

5 

09-46 

—006 

20  -70 

35-97 

5 

3 

10  -30 

—0  -90 

35  -97 

39-86 

5 

3 

09  -22 

+0-I8 

51  -52 

II  '75 

5 

5 

08-63 

+0-77 

03  -53 

16 -JJ 

4 

3 

09-71 

-0-31 

lb -41 

5I-.S5 

,<> 

3 

09-92 

-0-52 

Indiscriniiiiate  me 

-•:i=45'' 

11'  09" -38. 

Weighted 

mean 

--J5 

1 :    09    -4od[zO' 
'•67. 

'-06. 

243  observatiori.s,  ^ 

--.•]  pairs. 

llledii'-tiou 

tc  /L=o 

"•oc.? 

THK    ASTRONOMIC   MEASURES. 


•^0 


2.  Cooper,  Maine. —E.  Goodfcllow.  Zenith  telescope  No.  5.  September  S  to  18,  1859.  One 
division  of  level  =0"  "96  from  observations  at  this  station.  One  turn  of  micrometer=4i''' '416  from 
circumpolar  observations  at  this  station. 


Pairs  of 

stars. 

6  365 

6  372 

6  404 

6  428 

6  473 

6  476 

6  497 

6  5(X) 

6  491 

6  496 

6  542 

6  586 

6  602 

6  612 

6  657 

*6  662 

*6  662 

6674 

*6  662 

6  676 

6  730 

*6  817 

6  734 

*6  S17 

6  857 

6  895 

*6  930 

6  940 

*6  930 

6  943 

*6  957 

6  970 

*6  957 

7  024 

*6  957 

7  051 

7  060 

7  131 

7  152 

*7  176 

*7   176 

7   194 

7  213 

7  262 

7  26S 

*7  333 

7  301 

*7  333 

7  42S 

7  444 

7  455 

7  477 

7  501 

7  503 

7  533 

7  56S 

7  595 

7  607 

7  611 

7  627 

7  693 

7  708 

7  721 

*7  749 

7  731 

*7  749 

7  789 

7  798 

7  803 

7  845 

7  8S0 

7  888 

7  913 

7  950 

A(loi)te(l  s 
int-aii  N 

sconds  of 
.  P.  D. 

n' 

IV 

Latitude. 

V 

// 

II 

0 

/            // 

II 

42-25 

06-93 

6 

12       44 

59     13  -06 

— 046 

28  w 

32  -64 

6 

12 

12  -42 

+  0-18 

33  ■20 

54  -70 

6 

12 

12-55 

+005 

57-59 

04  -66 

4 

9 

12  -20 

+0-40 

05  -02 

'5-97 

2 

6 

13  35 

-0-75 

54  •"'> 

26-25 

5 

II 

12  -24 

+0-36 

30-86 

II  -47 

5 

II 

13-02 

—0-42 

19-92 

24  -50 

5 

5 

12 -98 

-0-38 

24-50 

04-41 

6 

6 

II  -97 

+0-63 

24-50 

09-87 

6 

6 

12  -04 

+  056 

33  -80 

25-32 

6 

8 

12    21 

+  0-39 

14  -20 

25-32 

6 

8 

12-03 

+0-57 

32 -78 

10  "09 

6 

12 

12-75 

-0-15 

55-22 

40  -40 

6 

8 

12-67 

—0  -07 

55-22 

32-27 

6 

8 

12  -70 

— 010 

48  -49 

51  -27 

6 

6 

12  -21 

-to -39 

48  -49 

22  -70 

6 

6 

II  -88 

+  0-72 

48-49 

19-74 

6 

6 

13  -05 

-045 

36-32 

04  -62 

4 

9 

12  -10 

+  0  -.50 

27-25 

12-79 

6 

S 

12-66 

—  0-06 

12-79 

35-04 

6 

8 

12-37 

+0-23 

3'  -52 

21  -73 

6 

12 

12-44 

+  0-16 

15  -44 

58  -81 

6 

8 

13 -oS 

—  O-4S 

40-50 

58-81 

6 

8 

12  -Si 

—0  -21 

30-58 

49-10 

6 

12 

12-48 

-fO-12 

41-58 

38  -88 

6 

12 

13-11 

-0-51 

12-63 

48-21 

5 

II 

12  19 

+0-41 

03-43 

33-26 

6 

12 

12-65 

— 005 

44-38 

.=io  -73 

6 

12 

II  92 

+0-6S 

06  -91 

12-34 

6 

12 

12  -34 

+0-26 

09-71 

19-01 

6 

12 

13  -35 

-0-75 

53-76 

34  -68 

6 

8 

13  -02 

-0-42 

43-18 

34  -68 

6 

8 

13  19 

—0  -59 

06-30 

42-31 

6 

12 

12  32 

+0-2S 

50-58 

49  -58 

5 

II 

13  -00 

—0  -40 

39  -73 

54-17 

6 

12 

13  -39 

-0-79 

39  -83 

3 1  -60 

6 

12 

12  "22 

+0-38 

scriminate  mean  =  44" 

59' 

12"  59. 

jhted  me; 

ui            =44 

59 

12     -603:0" 

-05- 

-52. 


209  ob.servations,  37  pairs. 

[Reduction  to  J^  =  -r  o"  -04.] 


3-  Hiitnpback, Maine 

division  of  level 

=  0''  -66 

station. 

Pairs  of  stars. 

5  628 

5  677 

5  747 

5  So  I 

5  SS6 

*5  937 

5  S95 

*5  937 

5  990 

5  997 

6  013 

6  109 

6  246 

•■6  349 

6  25S 

*6  349 

6  364 

6  428 

6  404 

6  476 

6  497 

6  500 

6  553 

6  601 

6  697 

6  711 

6  731 

*6  754 

*6  754 

6  779 

6  817 

6  S95 

6  930 

6  943 

6  957 

6  970 

6  9S5 

7  022 

*7  062 

7    lOI 

*7  062 

7   i'4 

7  152 

7   176 

7  204 

7  281 

7  306 

7  3'7 

7  39S 

7  44S 

7  469 

7  477 

7  4S9 

7  505 

7  533 

^7  568 

*7  542 

7  623 

*7  542 

'*7  56S 

7  683 

7  721 

7  731 

7  749 

7  789 

7  79S 

7  «43 

7  S48 

7  8S0 

7  888 

7  913 

7  950 

7  999 

8  023 

THE   EASTERN    OBLIQUE   ARC. 

-A.  T.  Mosman.     Zenith  telescope  No.  5.     July  26  to  August  19,  1858.     One 
One  turn  of  micrometer  =  41"  '416  from  circumpolar  observations  at  this 


Adopted 
mean 

seconds  of 
N.  P.  D. 

n' 

rt' 

I.atitude. 

V 

// 

// 

0      /          // 

// 

28-68 

07  -80 

8 

13 

44  51   47-33 

+  0-23 

24  73 

02  -21 

8 

13 

47-32 

+  0-24 

14  -84 

31  'oo 

S 

9 

48  -28 

—0-72 

10  '07 

31   -GO 

7 

9 

47  -16 

+  0  -40 

57 '91 

28-45 

8 

13 

46-99 

+  0-57 

06  ■91 

24-09 

8 

13 

47-23 

+  0-33 

46  -63 

07  -40 

8 

9 

47-78 

—  0  -22 

58  '60 

07  -40 

8 

9 

47-68 

—  0  -12 

34-31 

36  -50 

5 

12 

47-40 

+  0-16 

31  -92 

59  -oo 

5 

12 

48 -II 

-0  -55 

02  -32 

rig  -46 

8 

13 

47-28 

+  0-28 

10  -36 

19-83 

8 

13 

47-30 

-fo-26 

16-63 

42-70 

8 

13 

47-43 

H  0-13 

01  71 

36  -42 

8 

9 

47-60 

—0  -04 

36-42 

50-04 

7 

9 

47-03 

-fo-53 

34  -24 

19-90 

8 

13 

47-70 

-0-14 

05  -46 

42  -80 

10 

14 

47-66 

— o-io 

59-05 

02-73 

8 

13 

46-76 

+0  -80 

12  -07 

44  -87 

8 

13 

47-17 

+0-39 

09  -98 

37  -80 

9 

9 

47-28 

+0  -28 

09  -98 

22  -64 

9 

9 

46-88 

+0-6S 

39  -50 

25  -53 

10 

14 

47-64 

—0  -08 

34-47 

28-63 

9 

14 

47-24 

+0  -32 

01  -42 

03  -81 

8 

13 

47  -58 

—0  -02 

55  -77 

07  -85 

8 

13 

47-94 

—0  -38 

00-53 

54-45 

8 

13 

47-93 

-0-37 

20  -09 

03  -20 

8 

13 

48-04 

-0-48 

19  '60 

49-35 

9 

9 

47-30 

-fo-26 

27-70 

09  -63 

8 

9 

48-18 

— 0-62 

2770 

49-35 

7 

6 

47-54 

+0-02 

01  -20 

II  -22 

8 

13 

48  -40 

--0  -84 

00  73 

52-37 

9 

14 

48-13 

-0-57 

24  -3 1 

m  -34 

9 

14 

47-50 

+0  -06 

10-59 

38-90 

6 

12 

47  -56 

0  -00 

58-30 

12-75 

8 

13 

47-80 

—0  -24 

58-56 

50-46 

9 

14 

47-24 

+0-32 

25-40 

io-i8 

8 

13 

48  -lo 

-0-54 

criminate  mean  = 

44°  51 

'  47"-55- 

hteil  mean            = 

44     51 

47      -56  : 

t  o"-o5. 

C  = 

±o"-- 

)6. 

296  observations,  37  pairs. 

[Reduction  to  A  =  — 0^^-43.] 


i 


THE    ASTRONOMIC    MEASURES. 


25; 


4.  Bangor,  Maine.      E.  Goodfcllow.      Zenilli  telescope  No.  5.     Septeml 
One  division  of  level  =o''''S6.     One  turn  of  micrometer  =4i'''''397- 


er  7  to  October  10,  1S.57. 


I 'airs  0 

stars. 

6  427 

6  477 

6  496 

6  497 

6  500 

6  534 

6  579 

6  593 

*6  697 

6  711 

*6  697 

6  765 

6  771 

6  824 

6  849 

*6  881 

6  S60 

*6  881 

6  930 

6  944 

6  959 

7  001 

7  027 

*7  062 

*7  062 

7  114 

7  171 

7  219 

7  233 

7  253 

7  290 

7  306 

7  398 

7  448 

7  455 

*7  477 

*7  477 

7  480 

7  488 

7  505 

7  548 

7  565 

7  623 

7  708 

*7  668 

7  721 

*7  668 

7  731 

*7  727 

7  743 

*7  727 

7  770 

7  749 

7  843 

7  S75 

*7  914 

*7  914 

7  973 

7  999 

S  023 

8  059 

*S  118 

8  082 

*8  118 

8  126 

8  171 

8  279 

*8  374 

8  33S 

"•8  374 

46 

log 

So 

164 

*254 

310 

*254 

321 

263 

335 

395 

450 

Adopted  .seconds  of 
mean  N.  P.  D. 

// 

// 

4f)  'So 

38  -79 

25  -33 

"7  -"5 

14  -26 

59  -63 

43  '94 

■7-87 

24  ■  1  1 

50-24 

24-11 

01  -cS3 

19  63 

24  -22 

27  -82 

05  -78 

27  "48 

05  -78 

'570 

44-21 

54  '82 

30  -58 

45  "2o 

21    96 

21  -96 

34  -80 

44  19 

38-12 

52  -89 

08  -96 

01  32 

15  -33 

10 '65 

23-15 

12  -40 

10  -02 

ID  '02 

iS  -72 

09  '62 

19-17 

53 '03 

50-24 

26-31 

53  -84 

30-54 

28  -68 

30  '54 

18  -35 

54  '43 

17-33 

54 '43 

14-68 

09-97 

28  -90 

35  '6' 

15  -26 

15  -26 

46  -55 

44-54 

29-46 

57  -50 

23  -82 

27  -So 

23-82 

07-92 

28-62 

47  -87 

03  -23 

06  -88 

03  -23 

42  -28 

13-48 

42-58 

54  -68 

32  '53 

04  -91 

32  -53 

07  -83 

31  -24 

33  -09 

19-90 

41  -40 

10 
7 
7 

10 

7 
7 

10 
6 
6 
10 
10 
7 
7 

10 
10 
10 
10 

7 

6 

10 

10 

ID 

6 
7 
5 
6 
10 
6 

7 

10 
6 

7 
10 

7 
7 

10 
10 
5 
5 
8 
10 


44  48 


ide. 


I  -88 

■  0  99 

3  -07 

—0  20 

2  -02 

-  0  -8.5 

2  -27 

^0  -60 

3-07 

— 020 

2-55 

4  0  -32 

3-45 

-0  -58 

2-68 

-  0  -19 

2-91 

-0  -04 

2-85 

ro  02 

3-'i 

—0-24 

2-93 

0  06 

2-34 

-0  -53 

2  99 

—0-12 

2-80 

—  0  07 

2-46 

■4-0-41 

3-23 

—0  -36 

3  -54 

—0-67 

2-62 

4-0-25 

2  -21 

-I-0-66 

1  -97 

—0  -90 

3-17 

—0  -30 

3  39 

-0-52 

3-31 

-0-44 

3 -21 

-0  -34 

3-36 

-0-49 

2-37 

—0-50 

3  "02 

-0-I5 

2-78 

+0-09 

3-07 

— 020 

2-71 

-0-16 

3-44 

-0  -57 

3-89 

—  I  02 

3-82 

-095 

3-19 

-0  -32 

3  ->9 

—0  -32 

3  -00 

--0-I3 

3 -'3 

—0-26 

2-67 

-rO-2o 

2-70 

-rO-I7 

2  -27 

~-o  -60 

4193 — No.  7- 


Indiscriminate  niean=44°  48'  i2"-9o. 
Weighted  moan  =44    48    12   -87^:0" -05. 

,.=  ±o"-3S. 
213  observations,  41  pairs. 

[Reduction  to  A=o"-co.] 
—  17 


258 


THE    EASTERN    OBLIQUE    ARC. 


5.  Fariiih/g-/oi/,  Maine. 
Oue  division  of  level  =  o''' 


C.  O.  Boutelle.     Zenith  telescope  No.  5.     October  8  to  Noveml)er  6,  1866. 
90.     One  turn  of  niicronieter  =  4i^''48. 


Pairs 

of  stars. 

6   599 

6  697 

6  723 

6  806 

6  824 

6  875 

6  928 

6  937 

6  973 

7  024 

7  091 

7   114 

7  233 

7  241 

7  253 

7  306 

7  36« 

7  3S7 

7  444 

7  449 

7  474 

7  482 

7  524 

7  560 

7  627 

7  700 

^  746 

7  765 

7  S45 

7  850 

7  888 

7  901 

7  950 

7  9S3 

7  994 

8  059 

S  037 

8  082 

S  114 

8   118 

8  159 

8  188 

8  212 

8  231 

8  279 

8  284 

4 

46 

67 

83 

158 

201 

244 

2S5 

314 

334 

425 

441 

492 

540 

610 

647 

691 

7(X) 

721 

786 

Adopted 
mean 

seconds  of 
N.  P.  D. 

«' 

n 

// 

12  -Q 

167 

5 

56-4 

34-6 

5 

03  '5 

237 

6 

45 '5 

II   -Q 

7 

42-6 

03-2 

7 

51  -o 

44 '6 

6 

54-2 

38-6 

6 

08  'o 

10-4 

6 

16 -6 

16  -Q 

6 

03  -6 

51  "5 

6 

48-6 

30-0 

6 

04-6 

157 

6 

15-4 

27-4 

8 

167 

57 '4 

8 

41  "5 

46  -o 

7 

44  7 

46-8 

7 

21  -5 

46  -o 

5 

37-6 

01   -Q 

6 

51  7 

31  '5 

6 

00  'o 

27-4 

5 

02-5 

22  -S 

6 

07  "O 

12-6 

7 

48-0 

II  -o 

6 

57-5 

42  -Q 

6 

25-1 

46-5 

6 

i8-o 

467 

6 

14  'O 

55-6 

6 

187 

26-5 

6 

18 -4 

06-3 

6 

48-4 

23  'O 

5 

51  "4 

107 

5 

56-0 

09 '5 

5 

II  -6 

55  7 

5 

w 

Latitude, 

V 

0       /        // 

// 

5 

44  40  19 '49 

+0-05 

5 

19-85 

-0-31 

6 

19-40 

+0-I4 

6 

20  -06 

-0-52 

6 

1879 

+0-75 

6 

19-27 

+0-27 

6 

19-78 

-0-24 

6 

19-40 

+0-14 

6 

19-09 

+0-45 

6 

19 '05 

+0-49 

6 

19  "26 

+0-2S 

6 

19-97 

-0-43 

6 

19  -01 

+0-53 

6 

18-37 

+  1-17 

6 

19  "57 

-0-03 

6 

20  -17 

—0-63 

5 

20  -29 

-0-75 

6 

19-27 

+0-27 

6 

19  -02 

+0-52 

5 

20-38 

-0-S4 

6 

19 '43 

-t-o-ii 

6 

19-27 

+0-27 

6 

19-70 

—0  -16 

6 

19 '52 

-fo-02 

6 

20-07 

-0  -53 

6 

18-67 

+0-S7 

6 

19-77 

-0-23 

6 

18-96 

+0-58 

6 

1973 

—0  -19 

5 

18  -64 

+0-90 

5 

19  -00 

+0-54 

5 

19-70 

—0-16 

5 

19 '55 

— O-QI 

THE    ASTRONOMIC    MEASURES. 


259 


5.   Fann!)if{lo)i,  Maine — conliiiue'l. 


% 


Pairs  0 

f  stars. 

Adoptee 
mean 

seconds  of 
N.  P.  D. 

n' 

7V 

Latitude. 

V 

/r 

// 

0      / 

// 

// 

6  930 

6 

944 

43  "4 

07 '5 

7 

6 

44  40 

20  -06 

-0  52 

6  996 

7 

062 

03  0 

36-2 

8 

6 

19  46 

-o-o8 

7  o'^S 

7 

101 

51-6 

cxj  '5 

6 

6 

19  57 

—0  -03 

7   17' 

7 

254 

50-0 

28-6 

s 

6 

19-91 

-037 

7  278 

7 

3'3 

05-6 

06  'O 

7 

6 

'9-35 

-ho  -19 

7  365 

7 

373 

00  'O 

05  -o 

7 

6 

19  45 

+0-09 

7  399 

7 

401 

51  'o 

53 'o 

6 

6 

18-26 

+  1  -28 

7  469 

7 

477 

57-0 

50-0 

6 

6 

20  -23 

—0-69 

7  4SS 

7 

505 

47-8 

56-0 

7 

6 

19  "45 

-fo-09 

7  548 

7 

554 

27 '5 

07  '2 

6 

6 

2o-i8 

—0-64 

7  565 

7 

598 

22-5 

35  "o 

7 

6 

18  -86 

+0  -68 

*7  668 

7 

721 

55  7 

52-5 

6 

4 

19-96 

-0-42 

*7  668 

7 

73' 

55  7 

43 'o 

5 

4 

19  -10' 

-fo-44 

7  753 

7 

813 

18 -8 

50-1 

6 

6 

18-86 

+0  -68 

7  S55 

7 

9>5 

20 -6 

25-8 

6 

6 

19 '59 

— 005 

7  958 

7 

967 

18 -5 

14-2 

6 

6 

19-29 

-rO-25 

8  023 

8 

126 

36-0 

10-5 

6 

6 

19-88 

-034 

8  158 

8 

211 

59 '3 

36-0 

7 

6 

18-66 

4-o-SS 

8  224 

8 

237 

03-5 

28-0 

6 

6 

19-51 

+0-03 

52 

79 

44-5 

22  '2 

6 

6 

20  --2 

—0-48 

173 

232 

37-6 

22-8 

6 

6 

20  -57 

-1-03 

239 

299 

44-1 

19-5 

6 

6 

20-36 

-0-S2 

395 

450 

27  -o 

52 -s 

6 

6 

■9 '36 

+0-IS 

5S8 

630 

56-3 

43-3 

6 

6 

iS-26 

+  1  -28 

668 

679 

21  -6 

45-2 

6 

6 

20  -Sr 

-I  -27 

705 

727 

03-8 

48-5 

6 

6 

19 '54 

0  -00 

785 

87. 

31  -o 

05  -o 

5 

5 

20-58 

-I  -04 

962 

963 

04 '5 

46-5 

5 

5 

20  -76 

—  I  -22 

981 

995 

00 'O 

44-4 

5 

5 

20 -58 

-I  -04 

I  006 

I 

083 

12-6 

01  -3 

6 

6 

iS-49 

-f-I  '05 

I   129 

I 

139 

39 'o 

51  '5 

6 

6 

20-02 

-O-4S 

I  219 

I 

254 

49  7 

57-5 

6 

6 

20  -42 

-o-SS 

Indiscriminate  mean 
Weighted  mean 

e 
397  observations,  65 
[Reduction 

44°  40' 
=44    40 
==to"-55 
Dairs. 
to  ^  =0" 

i9"-55. 

19    •54±:o""05. 

•00.] 

26o 


THE   EASTERN   OBLIQUE   ARC. 


6.  iMouiit  Harris,  Maine. — G.  W.  Dean.  Zenith  telescope  No.  2.  First  series.  August  15  to 
24,  1S55.  One  division  of  level  =i"'i6.  One  turn  of  micrometer  =44'''8o3  from  circumpolar  obser- 
vations at  this  station. 


Pairs  of  .stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

n' 

w 

I^atitiide. 

7' 

// 

// 

0      /         // 

// 

5  S40 

5 

922 

35  '25 

36-72 

5 

II 

44  39  54  -25 

+  0-44 

6  129 

6 

218 

26^04 

05  -44 

5 

II 

55-20 

-0-51 

6  232 

6 

3fi 

37-00 

04-40 

3 

9 

54-88 

—  0-19 

6  237 

6 

318 

2470 

48  -24 

3 

9 

54-32 

+  0-37 

6  335 

6 

394 

30-40 

16  -96 

3 

9 

54-12 

+  0-57 

6  372 

6 

,392 

19  -81 

38-24 

2 

7 

55  -08 

-0-39 

6  419 

6 

466 

10-93 

58-34 

5 

II 

55-07 

-0-38 

*6  477 

6 

497 

47-66 

16-62 

3 

6 

54-04 

+  0-65 

*6  477 

6 

553 

47-66 

25-85 

2 

5 

55-18 

-0-49 

^6  623 

6 

651 

51  -94 

54-43 

5 

7 

54-43 

+0-26 

*6  623 

6 

667 

51  -94 

12-59 

5 

7 

53  -95 

+0-74 

6  711 

6 

723 

05  '36 

21  -21 

5 

II 

54-92 

-0-23 

6  731 

6 

754 

25  -28 

00  -98 

5 

II 

54-82 

-0-13 

6  824 

6 

875 

42  -20 

09  -08 

5 

II 

54-73 

—0-04 

6  92S 

6 

937 

41  -81 

05-18 

6 

II 

54-45 

+0-24 

6  973 

■'7  024 

40-25 

08-02 

6 

7 

54-11 

+0-58 

6  978 

*7 

024 

03  -28  . 

08  -02 

4 

7 

55-01 

-0-32 

7  062 

■■'7 

114 

45-20 

58-23 

5 

7 

53  -98 

+0-71 

7  091 

/ 

114 

02  -02 

58  -23 

5 

7 

54-62 

+0-07 

7  233 

7 

241 

19  -18 

06  -ID 

5 

II 

54-90 

—  0  -21 

7  253 

7 

306 

35  -81 

43-49 

5 

II 

54-92 

-0-23 

7  368 

7 

3S7 

56  -50 

58  -31 

5 

II 

54-36 

+0-33 

7  399 

7 

401 

35-19 

36  -22 

5 

II 

54-30 

+0-39 

7  469 

7 

477 

46  -90 

41  -iS 

4 

10 

55-64 

-0-95 

7  488 

7 

505 

41  -12 

50-84 

5 

II 

55-31 

—0-62 

7  524 

7 

560 

00  -92 

14-76 

5 

II 

55-47 

-0-78 

7  571 

*7 

61 1 

10-83 

13-60 

5 

7 

54-19 

+0-50 

7  584 

*7 

611 

58  -95 

13-60 

5 

7 

54-20 

+0-49 

7  651 

7 

693 

43  -49 

18  -07 

5 

II 

54  -98 

—0  -29 

7  746 

7 

765 

30-45 

12  -20 

5 

II 

54-22 

+0-47 

7  845 

7 

850 

02-93 

07-71 

5 

II 

54  -86 

-0-17 

7  9*52 

*7 

999 

47  -80 

22-81 

3 

6 

55-14 

-0-45 

*7  999 

8 

023 

22  -Si 

08  -00 

2 

5 

55-49 

-o-8o 

8  037 

8 

082 

24-29 

06-94 

4 

10 

53  -83 

+0-86 

8  114 

8 

128 

35-50 

53  -70 

5 

1 1 

54-72 

—0  -03 

8  156 

*8 

188 

55-49 

00-36 

5 

7 

54-44 

+0-25 

8  159 

*8 

188 

39-44 

00-36 

5 

7 

54-79 

—0  -10 

8  212 

8 

231 

45-25 

5'  -97 

5. 

II 

55-08 

-0  -39 

8  237 

8 

261 

06-22 

04-35 

5 

II 

54-33 

+0-36 

8  279 

8 

284 

I 

27-94 
ndiscriminate 

51  -44 
mean     = 

4 
=44°  39'  54 

10 

''-68. 

54-81 

—0-12 

A 

Veighted  mean               = 

=44    39   54 

-69^ 

=0^^-05. 

e- 

=  ±o"-37. 

I 

79  observations,  40  pai 

rs. 

THE   ASTRONOMIC   MEASURES. 


261 


6.  Moinil  Harris,  Maine.  — G.  W.  Dean.  Zenith  telescope  N 
27.  1855.  One  division  of  level  =0"  '632,  from  observations  at 
meter  =39"  '522  from  circumpolar  observations  at  this  station. 


o.  10.     Second  series.     August  6  to 
this   station.     One  turn  of    tnicro- 


rains  of  stars. 

5  731 

5  797 

5  Ho 

5  922 

5  944 

6  036 

6  129 

6  21S 

6  232 

6  31 1 

6  237 

6  31S 

6  335 

6  394 

6  372 

6  392 

*6  419 

6  456 

*6  419 

6  466 

*6  477 

6  497 

*6  477 

6  553 

6  566 

6  581 

*6  623 

6  651 

*6  623 

6  667 

6  711 

6  723 

6  73> 

6  754 

6  824 

6  875 

6  92S 

6  937 

6  973 

*7  024 

6  978 

*7  024 

7  062 

*7   114 

7  091 

*7   'H 

7  233 

7  241 

7  253 

7  306 

*1  368 

7  377 

*7  368 

7  387 

7  399 

7  401 

7  469 

7  477 

7  488 

7  505 

7  524 

7  560 

7  57' 

*7  611 

7  584 

*7  611 

7  651 

7  693 

7  746 

7  765 

7  789 

7  798 

7  S45 

7  850 

7  879 

*7  888 

7  880 

*7  SSS 

7  9'3 

7  950 

7  962 

*7  999 

*7  999 

8  023 

8  037 

S  0S2 

Adopted  seconds  of 
mean  N.  r.  I). 

71 ' 

IV 

Latitude. 

V 

// 

// 

0      /         // 

// 

25  '48 

26-99 

5 

16 

44  39  54  -99 

-0  -48 

35  -25 

36-72 

6 

[7 

54-13 

+0  -3cS 

05  -ss 

09  -54 

5 

16 

54-37 

-}-o-i4 

26  '04 

05  -44 

5 

16 

54  -66 

-0-15 

37 -dO 

04  -40 

5 

16 

54-81 

-0-30 

24  •70 

48  -24 

4 

15 

54-41 

+  0    ID 

30  •4() 

16-96 

3 

'4 

54-61 

— 010 

19 -Si 

38-24 

2 

1 1 

54-52 

— Q-OI 

10-93 

24  -22 

5 

II 

55  -38 

-0  -S7 

10  '93 

58-34 

5 

II 

55-15 

—0-64 

47-66 

16-62 

5 

1 1 

53  -65 

+0  -86 

47-66 

25  -85 

5 

II 

54-76 

-0  -25 

05  -37 

03  -90 

5 

16 

54  -84 

-0-33 

51  94 

54  -43 

5 

II 

54-77 

—0  -26 

51  '94 

12-59 

5 

II 

54-70 

—0  19 

05  '36 

21  -21 

6 

17 

54  -73 

—0  -22 

25  -28 

00  -98 

6 

17 

54-19 

+0-32 

42  -20 

09  -08 

6 

17 

54  -36 

+0-15 

41  -81 

05  -18 

5 

16 

54-44 

+  0-07 

40-25 

08  -02 

6 

II 

54-63 

—012 

03  -28 

oS  "02 

6 

u 

55-01 

— o-5» 

45 '20 

58  -23 

6 

II 

53-97 

+0-54 

02  -02 

58  -23 

6 

II 

54  -38 

^0-13 

19  -iS 

06  "lo 

6 

17 

54-18 

+0-33 

35-8. 

43-49 

5 

16 

54-58 

— 007 

56  •5<-> 

31  -10 

5 

11 

54-24 

+0-27 

56-50 

58-31 

5 

II 

54  -29 

-fo-22 

35-19 

36  -22 

5 

16 

54  -05 

+0-46 

46-90 

41  -1.8 

6 

17 

54  57 

-006 

41  '12 

50   84 

6 

17 

54  -79 

-0  -28 

00  -92 

14-76 

6 

17 

54-69 

—0  -iS 

10  -83 

13  -60 

6 

1 1 

54  -22 

-fo-29 

58  -95 

13  -60 

6 

II 

54  -37 

~o-i4 

43  -49 

18-07 

6 

'7 

54-76 

-0-25 

30  -45 

12    20 

5 

16 

53  -77 

+0-74 

18-05 

53  '50 

5 

16 

54  43 

-o-oS 

02  -93 

07-71 

4 

15 

54-12 

-^  0  -39 

16  69 

08  -20 

3 

9 

54  -48 

-  P  05 

54  02 

oS  -20 

2 

8 

54  -34 

-0-17 

54-44 

46-74 

5 

16 

54-41 

+0M0 

47  -80 

22  -81 

5 

II 

54  -85 

-0  -34 

22-81 

oS  -ix) 

5 

II 

55  -34 

-0-83 

24  -29 

06  -94 

5 

16 

54-11 

-fo  -40 

262 


THE    EASTERN    OBLIQUE    ARC. 


6.  Alount  Harris,  Maine.     Second  series — continued. 


Pairs 

of  stars. 

.Adopted  seconds  of 
mean  N.  P.  D. 

n' 

w 

Latitude. 

V 

// 

// 

0       /          // 

// 

8   114 

8   128 

35  "50 

53-70 

5 

16 

44  39  54  -83 

-0-32 

8   156 

''8   188 

55-49 

00-36 

5 

II 

54-23 

+  0-28 

8  159 

-'8  188 

39 '44 

00-36 

5 

II 

54-69 

-0-18 

8    212 

8  231 

45 '25 

51  -97 

5 

16 

54-41 

+0-10 

S  237 

8  261 

06  -22 

04-35 

5 

16 

54-20 

to -31 

8  279 

8  284 

27-94 

51  "44 

5 

16 

55-13 

—0  -62 

Indiscriminate  mean  =44° 
Weighted  mean            =44 

f=d=o 
248  observations,  49  pairs. 

// 

39' 
39 

29. 

54'' 
54 

-52 
-51 

zbo'^  -04. 

6.  Mount  Harris,  tisane. — E.  Goodfellow.     Zenith  telescope  No.  10.     Third  series.     September  12 
to  25,  1S55.     One   division  of  level=o"-632.     One  turn  of  micronieter=39"-507  from   circumpolar 


observations  at  this 

station. 

Pairs 

of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

?i' 

yj 

Latitude. 

V 

// 

// 

0      /         // 

// 

*6 

419 

6 

456 

10-93 

24  -22 

I 

2 

44  39  54  -74 

-fo-05 

*6 

419 

6  466 

10-93 

58  -34 

I 

2 

54-09 

+0-70 

*6 

477 

6 

497 

47-66 

16-62 

5 

6 

54-17 

+0  -62 

*6 

477 

6 

553 

47-66 

25  -85 

5 

6 

55-24 

-0-45 

6 

566 

6 

581 

05  -37 

03-90 

6 

9 

55-02 

-0-23 

*6 

623 

6 

651 

51  -94 

54  -43 

6 

6 

54-86 

—0  -07 

*6 

623 

6 

667 

51  -94 

12-59 

6 

6 

54  -74 

+0-05 

6 

711 

6 

723 

05-36 

21  -21 

5 

9 

54-43 

+0-36 

6 

73T 

6 

754 

25  -28 

00-98 

5 

9 

55-50 

-0-71 

6 

S24 

6 

875 

42  -20 

09-08 

6 

9 

54-74 

+0-05 

6 

928 

6 

937 

41  -81 

05-18 

6 

9 

54  -45 

+0-34 

6 

973 

^7 

024 

40-25 

08  -02 

6 

6 

54-42 

+0-37 

6 

978 

*7 

024 

03  -28 

08  -02 

6 

6 

54-30 

+0-49 

7 

062 

7 

114 

45-20 

58  -23 

6 

9 

54-88 

—0  -09 

7 

233 

7 

241 

19-18 

06  -10 

6 

9 

53-74 

+  1  -05 

7 

253 

7 

306 

35  -81 

43 '49 

6 

9 

55-44 

—0-65 

*7 

368 

7 

377 

56  -50 

31  -ID 

5 

6 

54-12 

+0-67 

*7 

368 

7 

387 

56-50 

5^-31 

6 

6 

54-59 

+0-20 

7 

399 

7 

401 

35-19 

36  '22 

6 

9 

54-37 

+  0-42 

7 

469 

7 

477 

46  -90 

41  -18 

6 

9 

55-30 

-0-51 

7 

488 

7 

505 

41  -12 

50-84 

6 

9 

55-45 

-0-66 

7 

524 

7 

560 

00  -92 

14-76 

6 

9 

54-91 

—0-12 

7 

571 

*7 

611 

10-83 

13-60 

4 

5 

54-66 

+0-13 

7 

584 

7 

611 

58-95 

13-60 

7 

6 

54  -59 

-l-o  -20 

7 

651 

7 

693 

43  -49 

18  -07 

6 

9 

55-02 

-0-23 

7 

746 

7 

765 

30-45 

12    20 

6 

9 

53-80 

+0-99 

7 

789 

7 

798 

18-05 

53  -50 

6 

9 

55-03 

—  0  -24 

7 

845 

7 

850 

02-93 

07  -71 

6 

9 

54-88 

—0  -09 

7 

S79 

*7 

888 

16  -69 

08  -20 

3 

5 

55-09 

—0-30 

THE    ASTRONOMIC    MEASURES. 


263 


6.   Moiinl  Harris,  Maine.     Third  series — conlinue'l. 


Pairs  of  stars. 

.\do])tc{l  secoiuls  of 
mean  N.  P.  U. 

n' 

VJ 

I 

,;iti 

tilde. 

V 

// 

// 

0 

/ 

// 

ff 

7  SSo 

*7  S88 

54  -02 

08 -20 

3 

5 

44 

39 

55-47 

-0-68 

7  9'3 

7  950 

54-44 

46-74 

6 

9 

55-00 

—0-21 

7  962 

*7  999 

47-80 

22  •8r 

6 

6 

55-23 

—0-44 

7  999 

8  023 

22  81 

08  -oo 

6 

6 

55  -92 

-I -'3 

8  037 

8  082 

24  29 

06  94 

6 

9 

54-37 

-1-0-42 

S   114 

8   1 28 

35  "50 

53  -70 

6 

9 

55  -28 

-049 

8  156 

*8  188 

55  -49 

00-36 

7 

6 

54-47 

+032 

8  159 

*8  188 

39-44 

00.36 

6 

6 

54-90 

—0  -II 

8  212 

8  231 

45  -25 

51  "97 

5 

9 

54  -89 

—  010 

8  237 

S'26r 

06  -22 

04-35 

6 

9 

53  -80 

+0-99 

8  279 

8  284 

27-94 

51  -44 

6 

9 

55  -38 

-0-59 

Indiscriminate  mean    = 

44° 

39' 

54" 

■78. 

Weighted  mean 

= 

44 

39 

54 

-79  =b  0" 

■05 

c  = 

±  0"  -44. 

21 

8  observations 

,  40  pairs. 

Collcclion  of  rcsulls  at  station,  Mount  Harris,  Maine. 

G.  W.  Dean,  Z.  T.  No.  2         <p : 

G.  W.  Dean,  Z.  T.  No.  10 

E.  Goodfellow,  Z.  T.  No.  10 

Mean  adopted  <p 
[Reduction  to  A=  +  o"  -21.] 


44°  39' 

54" 

•69  ±  0" 

-05. 

54 

•51  ±0 

•04. 

54 

•79  ±0 

•05. 

44     39 

54 

•66  ±0 

-04. 

7.  Howard,  Maine. — E.  Goodfellow.  Zenith  telescope  No.  5.  July  13  to  23,  1S59.  One  division 
of  level  =  i"-oi5  from  observations  at  this  station.  One  turn  of  micrometer  =  44"-4i8  from  circum- 
polar  observations  at  this  station. 

Adopted  seconds  of  , 

mean  N.  P.  D.  " 


Pairs  of  stars. 

*5  113 

5   122 

*5  113 

5   130 

5  210 

5  259 

5  244 

5  249 

5  307 

5  321 

5  388 

5  4'-To 

5  440 

5  459 

5  466 

5  514 

5  523 

5  568 

5  604 

5  643 

5  658 

5  747 

5  823 

5  883 

5  834 

5  937 

5  990 

5  997 

6  095 

*6  109 

*6  log 

6   162 

03-14 

02-30 

03  -14 

II  -88 

33  -98 

10  -14 

51  -44 

49-95 

49-85 

07-30 

37  -00 

08  -78 

53  -61 

07  -76 

46  -87 

53  -35 

20-48 

58  -80 

21  -97 

54  -20 

20-74 

30-21 

41  -88 

20-28 

45-90 

33 -85 

00-05 

28  -65 

08  -06 

24  -52 

24  -52 

'3  -58 

■V 

Latitude. 

V 

0     /        // 

// 

5 

44  37  48  -84 

4-0-40 

5 

48-46 

+078 

8 

48  -44 

-fo-So 

8 

48-85 

+039 

8 

49  43 

— 019 

9 

48  -85 

-039 

9 

49  59 

-0-35 

9 

48  -61 

-rO-63 

9 

49  58 

-0-34 

9 

49-06 

-018 

9 

49  "35 

—on 

8 

49-61 

-0  -37 

S 

49  42 

-o-iS 

9 

49-46 

— 022 

6 

48  -89 

+0-35 

6 

50  02 

-078 

264 


THE    EASTERN    OBLIQUE    ARC. 

7.   Ho7i<ard,  Maine — continued. 


Pairs  of 

stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

n' 

7V 

lyatitude. 

V 

// 

// 

0      /        // 

// 

6  231 

*6 

272 

43  ••'^S 

00  -41 

6 

6 

44  37  49  -45 

—0  -21 

*6  251 

*6 

272 

27-97 

00  -41 

7 

6 

50 -'3 

—  0  -89 

*6  316 

6 

322 

25  ••'^9 

07  -So 

7 

6 

49-32 

—  0  -08 

*6  316 

6 

341 

25  ■«9 

61  -60 

7 

6 

48-67 

+  0-57 

6  372 

6 

392 

06  -93 

23-96 

6 

9 

49-07 

+  0-17 

*6  419 

6 

456 

55  79 

08  '(X) 

5 

6 

50-00 

—  0-76 

*6  419 

6 

466 

55  79 

41  -82 

5 

6 

49  -7''^ 

-0-54 

6  476 

6 

493 

54  -68 

45-16 

4 

8 

48  -87 

fo-37 

6  477 

6 

553 

29  '8 1 

04  -95 

4 

8 

48  -72 

fo-52 

6  566 

6 

581 

44  -oo 

39  -63 

6 

9 

49  -03 

f-O  -21 

*6  623 

6 

667 

25-49 

44-64 

6 

6 

50-18 

-0-94 

*6  623 

6 

651 

25-49 

27-29 

6 

6 

49  -91 

-0  -67 

*6  723 

6 

806 

50-67 

34  -56 

6 

4 

49  -78 

0  -54 

*6  723 

6 

765 

50-67 

45-19 

6 

4 

49-79 

-0-55 

*6  723 

6 

S13 

50-67 

18-18 

6 

4 

49  -84 

—0  -60 

6  S24 

6 

875 

06  '26 

30-30 

6 

9 

49-00 

+0-24 

*6  928 

6 

937 

00  -92 

23  -23 

6 

4 

48  -9S 

j  0  -26 

*6  928 

6 

967 

00  -92 

24-65 

6 

4 

48-57 

+0  -67 

*6  928 

6 

997 

00  -92 

21  -93 

6 

4 

48  -26 

i  0  -98 

*7  027 

7 

062 

2  2-54 

58-26 

6 

6 

49-19 

fo  -05 

*7  027 

7 

091 

22-54 

14-19 

6 

6    . 

49-64 

—0  -40 

7  100 

7 

112 

15-10 

19  -JO 

6 

9 

-48-84 

+0-40 

7  233 

*7 

253 

26  -4.S 

42  -08 

6 

6 

49-52 

—0  -28 

*7  253 

7 

306 

42  -08 

47-5" 

6 

6 

49-40 

— o-i6 

In 
W 

2 

discriminate  mean     =  44° 
eighted  mean               =  44 

e  =d=o 
21  observations,  40  pairs. 

[Reduction  to  A  = 

37' 

37 

"-45 

-0' 

49"-26. 
49    -24  ± 

'■56.] 

o"-o5. 

8.  Mount  Desert,  Maine. — S.  Harris.  Zenith  telescope  No.  5. 
tember  5,  1856.  One  division  of  level  =0"  -73  from  observations  at 
eter  =41"  -42  from  circunipolar  observations  at  this  station. 

Adopted  seconds  of  ^^,  ^ 

mean  N    P.  D. 


5  15 

7  21 

6  18 

7  21 
6  18 

6  15 

6  27 

6  27 

6  27 


First  series.     August  18  to  Sep- 
this  station.     One  turn  of  microm- 


Pairs  of  stars. 

6  062 

*6  129 

6  068 

*6   129 

*6  255 

6  268 

*6  255 

6  357 

6  395 

*6  429 

*6  429 

6  522 

6  553 

6  583 

6  629 

6  637 

6  687 

6  722 

02  -90 

26  -14 

45-46 

26  -14 

57  -91 

07-44 

57-91 

23-53 

18  -80 

06-94 

06  -94 

47-75 

20  -45 

05  '45 

14  -87 

38  -62 

16-61 

23-34 

I^atitude. 

o      /  // 

44  2r  06 -38 

06  -56 

06  -5 1 

06  -33 

05  -85 
06-14 

06  -39 
06-19 
06-13 


+0-13 

-0-05 

O  -QO 

+  0-18 

+0  -66 
+0-37 

+  0  -12 
+  0-32 
+  0-38 


THE    ASTRONOMIC    MEASURES. 


26: 


8.   Mount  Desert,  Maine.     First  series — cc)nlimu 


I 


Pairs  of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

«' 

?</ 

r.atitude. 

V 

// 

// 

< 

3       /         // 

// 

*6  769 

6  799 

14-17 

48-16 

6 

18         44  21  <yi  -66 

-0-15 

*6  769 

6  830 

1417 

17-70 

6 

18 

06-50 

+001 

6  849 

6  865 

37  •(« 

58  -58 

6 

27 

06 -61 

-  o-io 

16  879 

6  932 

30-59 

'8-37 

6 

27 

06    1  I 

4  0  -40 

6  979 

6  994 

II  -65 

38  -32 

6 

27 

06  -29 

+  0  -22 

7  022 

7  062 

07  -50 

33-49 

6 

27 

06  -45 

-  o-f)6 

7  073 

7   '53 

24  -90 

42  -83 

4 

•9 

06  -73 

0  -22 

7  219 

7  253 

51  '17 

22-37 

4 

19 

06  -42 

+  0  -09 

7  220 

7  256 

10-37 

16-11 

5 

23 

06-34 

+  0-17 

7  3><' 

7  368 

23-23 

41  -98 

6 

27 

06  -40 

4  0  -u 

7  416 

7  461 

25  -02 

59  -25 

6 

27 

06-57 

—0  06 

7  521 

7  54« 

52-76 

09-52 

6 

27 

06  -42 

-^  0  -09 

7  569 

7  595 

20  -84 

33  -83 

6 

27 

06  -91 

—0  -40 

7  615 

7  623 

50  -84 

43  -"4 

6 

27 

06-68 

-0-17 

7  72" 

7  754 

46-19 

32-42 

6 

27 

07-04 

-0-53 

7  731 

7  77S 

35-83 

24-41 

7 

32 

06  99 

-0-48 

7  800 

7  803 

14-36 

44-64 

5 

23 

06-72 

—0  -21 

7  855 

*7  858 

24  -55 

35-05 

6 

18 

06  -80 

—0-29 

*7  S58 

7  8S2 

35  -05 

26-94 

7 

21 

06  -30 

-0  -21 

7  S94 

7  9'3 

52-06 

34-79 

6 

IS 

06  -02 

+  0.49 

8  141 

8   1 88 

32-05 

40  -54 

5 

23 

06  -99 

-0-48 

8  284 

8  344 

31  -40 

44  -73 

6 

27 

06  -60 

—0  -09 

S  366 

8  374 

17  -12 

22  -62 

7 

32 

06-44 

+0-07 

Indiscriniiiiatt'  mean 

=  44 

°  2 

'  06"  -48. 

We 

l^lited  tiieaii 

=  44 

2 

I     06     -5 1  d=  0 

"  -03. 

e 

=  d= 

0" 

■46. 

189 

observati 

ons,  32  pairs. 

[Reduction  to 

A  = 

"-SS.] 

8.  Mount  Desert,  Maine. — E.  Goodfellovv.  Zenitli  telescope  No.  5.  Second  series.  September 
iS  to  October  5,  1856.  One  division  of  level  =  o"  -716  from  observations  at  this  station.  One  turn  of 
micrometer  =  4i'''-42i  from  circumjwlar  observations  at  this  station. 


Pairs  of  stars. 


*6  255 
*6  255 

6  395 
*6  429 

6  553 
6  629 
6  687 
*6  769 
*6  769 
6  849 


6  268 

6  ,',57 
*6  429 
6  522 
6  583 
6  637 
6  722 
6  799 
6  830 
6  865 


doptetl  seconds  of 
mean  N.  P.  U. 

1/ 

" 

57  -91 

07  -44 

57  -91 

23-53 

18 -80 

06  -94 

06  -94 

47  -75 

20-45 

05  -45 

14-87 

38  -62 

16 -61 

23  -34 

14  -17 

48-16 

14-17 

17-70 

37-00 

58  -58 

w 

Latitude. 

V 

0      /        // 

// 

5 

44   21    06-25 

i-0-2S 

5 

06  06 

+0-47 

5 

05  -68 

+0-85 

5 

06  06 

+0-47 

8 

06  97 

-044 

8 

06  22 

+0-31 

8 

05-63 

+090 

5 

06  55 

— 002 

5 

06-43 

+o"io 

5 

06-55 

—0  02 

266 


THE    EASTERN    OBLIQUE    ARC. 


S.  Mount  Dcacii,  jNIaine.     Second  series — continued. 

n   •        f    .  Adopted  seconds  of  „,  .,,  Tot;f,.Ho 

Pairs  of  stars.  „,^^„  j^    p   j^  n  m  I.atUude, 


6  S79 

6 

932 

30-59 

18  -37 

7 

8 

44  21   06  -61 

-0-08 

6  979 

6 

994 

II  -65 

38  -32 

6 

S 

05-77 

+0-76 

7  022 

7 

062 

07-50 

33  '49 

6 

8 

06  -66 

-0-13 

7  073 

7 

'53 

24-90 

42 -S3 

5 

7 

06  -78 

-0-25 

7  2J9 

7 

253 

51  ■17 

22-37 

4 

7 

07  -32 

-0-79 

7  220 

7 

256 

10  -37 

]6  -II 

4 

7 

06  -14 

-fo-39 

7  310 

7 

368 

23  '23 

41  -98 

6 

8 

06-42 

+0  -11 

7  416 

7 

461 

25  -02 

59  -25 

6 

S 

06  -09 

+  0-44 

7  521 

7 

548 

52  -76 

09  -52 

6 

8 

06-73 

—0  -20 

7  569 

7 

595 

20  -84 

33  -83 

6 

S 

07-23 

-0  -70 

7  615 

7 

623 

50-84 

43-04 

7 

8 

06  -07 

-+0-46 

7  721 

7 

7,S4 

46-19 

32  -42 

6 

8 

07  -II 

-0-58 

7  731 

7 

778 

35  -83 

24-41 

6 

8 

07  -39 

-0-86 

7  Soo 

7 

803 

14  -36 

44-64 

4 

7 

07-73 

—  I  -20 

7  S55 

*7 

858 

24  '55 

35  -05 

6 

5 

06  -20 

+0  -33 

7  S58 

7 

882 

35  '05 

26-94 

6 

5 

06  -00 

+0-53 

7  S94 

7 

913 

52  -06 

34  -79 

6 

8 

06  -73 

—0  -20 

S  141 

8 

J  88 

32-05 

40-54 

6 

8 

07  -32 

-0-79 

S  2S4 

8 

344 

31  -40 

44-73 

6 

8 

06  -21 

^  0-32 

S  366 

8 

374 

17-12 

22  -62 

4 

7 

06  -19 

+0-34 

Indiscriminate  mean 

=  44° 

21'  06" 

-50. 

Weighted 

mean 

=  44 

21    06 
0"  -41. 

-53  =b  0"  -07. 

171  observations,  30  pairs. 
[Reduction  to  A  =  —  i" 

88.] 

9.  Ragged  Moi()!ta!)i,Ma.me. —G.y^.  'DcslU.  Zenith  telescope  No.  5.  First  series.  August  18  to 
September  7,  1854.  (Jne  division  of  level  =o''-7i  from  ob.servations  at  this  station.  One  turn  of 
micrometer  =  41^-426  from  circumpolar  observations  at  this  station. 


Pairs 

of  stars. 

5  596 

5  617 

5  795 

5  847 

5  874 

5  911 

5  922 

5  978 

6  006 

6  030 

6  052 

6  082 

6   177 

6  223 

6  241 

6  316 

6  395 

*6  429 

-6  429 

6  522 

6  534 

•■■6  583 

6  659 

6  711 

6  734 

6  806 

Adopted  seconds  of 
mean  N.  P.  D. 


02  -60 

50-57 

14-25 

JO  -82 

45  -86 

55-20 

33-71 

47  -28 

30-72 

40-79 

57  -22 

39  -45 

04  -82 

40  -99 

08  -99 

36  -74 

25-72 

14  -28 

14-28 

58  -88 

16-49 

17-41 

44  -88 

12  -92 

54-74 

18  -22 

n' 

~u 

Latitude. 

■    V 

0       / 

// 

// 

2 

9 

44  12 

43  -02 

—0  -ID 

4 

10 

43-17 

-0-25 

5 

10 

43  -45 

-0  -53 

5 

ID 

43  -50 

-0-58 

6 

II 

42-12 

+0  -80 

6 

I  I 

43-51 

-0-59 

6 

II 

42-94 

—0-02 

6 

II 

42-47 

+0-45 

6 

7 

43  -01 

—0  -09 

5 

7 

42  -65 

+0-27 

5 

7 

42  -26 

+0-66 

6 

II 

42-90 

+0  -02 

5 

ID 

42-47 

+0-45 

THE    ASTRONOMIC   MEASURES. 


267 


9.  Ragged  Mounla 

in,  Maine. 

First 

series — 

continued. 

Pairs 

of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

n' 

w 

Latitude. 

V 

// 

// 

0       /        // 

// 

6  763 

6 

813 

42-42 

03-10 

6 

II 

44  12  43-14 

— 022 

6  S24 

6 

9'5 

51  -20 

37  '67 

5 

7 

43-25 

-0-33 

*6  915 

6 

928 

37 '67 

52  -oi 

5 

7 

43 ''2 

—  0-20 

6  940 

7 

024 

3'  '54 

'9 '33 

5 

10 

43-45 

-0-53 

7  09S 

7 

126 

44 '25 

36-50 

6 

II 

43-11 

-0-19 

7   "71 

7 

253 

22   17 

49  -23 

6 

II 

42-71 

^0-2I 

7  278 

7 

336 

50  -85 

57-30 

6 

II 

42-84 

^o-o8 

7  385 

7 

448 

32-98 

09-03 

6 

II 

43  65 

-0  73 

7  512 

7 

566 

03  -20 

58  -74 

6 

1 1 

42 -82 

+010 

7  595 

7 

623 

06-75 

16-38 

6 

1 1 

43' 14 

— 022 

7  679 

7 

695 

1974 

29  -98 

6 

II 

42-41 

-0-51 

7  721 

7 

754 

21  -09 

07-98 

6 

II 

43 '32 

—0-40 

7  731 

7 

778 

10  96 

00-03 

6 

II 

43-56 

—0-64 

7  894 

*7 

983 

29-04 

34-41 

5 

7 

42  -75 

-0-17 

7  913 

*7  983 

13-08 

34-41 

5 

7 

42-41 

+0-51 

5  828 

5 

840 

08-28 

31  -00 

4 

10 

41  -84 

+  1  -08 

5  900 

5 

972 

29  -61 

20-83 

4 

10 

42-27 

-0-65 

6  056 

6  062 

51-88 

00  -75 

3 

10 

42-92 

000 

6  068 

6 

129 

43  '58 

26  00 

3 

10 

42-80 

-r  0  12 

6  079 

6 

178 

10 -S3 

40-90 

2 

9 

42-65 

+0-27 

6  234 

6 

318 

41  -27 

50-48 

5 

10 

43  09 

-0-17 

6  238 

6 

311 

46-34 

06-55 

5 

10 

43  "30 

-0-38 

6  477 

*6 

571 

52-10 

26-74 

2 

6 

42-84 

-0-08 

6  496 

*6 

571 

39-21 

26-74 

2 

6 

43  "43 

-0-51 

6  497 

■=^6 

583 

21  -36 

17-41 

2 

6 

43  '33 

—  0-41 

6  6S7 

6 

722 

30  -87 

38-90 

4 

10 

42  49 

-0  43 

6  740 

6 

867 

49-65 

34-41 

4 

10 

42  -82 

-hO-IO 

6  926 

6 

975 

33  73 

45  -95 

5 

10 

43  '53 

— 061 

6  986 

7 

076 

04  -20 

54-08 

5 

10 

43  -02 

—0  -io 

7  048 

7 

085 

29  -07 

13-97 

5 

10 

43  '3' 

-0-39 

7  243 

7 

337 

2975 

02  -50 

4 

10 

41  -49 

-^1-43 

7  569 

*7 

615 

53  '44 

24  -00 

I 

4 

43  -22 

-0  -30 

7  570 

*7 

615 

04-44 

24  -or; 

I 

4 

42-67 

-  0  -25 

7  782 

7 

843 

25  30 

24-04 

5 

10 

43  '45 

-0-53 

*7  855 

7 

879 

01  -25 

34  -92 

5 

7 

42-52 

—0  -40 

*7  855 

7 

8S0 

01  -25 

12  -50 

5 

7 

42-70 

-^0.  22 

Indiscriminate  mean  = 

44° 1 2' 

42"-92 

Weighted  mean            = 

=44  12 

42    -92 

±o"-o5. 

<'= 

:±     o"-25. 

228  observatiotis,  49  pa 

irs. 

[Red 

uction  tO:^  =  +o'''-40.] 

268 


THE    EASTERN    OBLIQUE    ARC. 


9.  Ragged  J\/o!i)itai  II,  Maxna. — S.Harris.  Zenith  telescope  No.  5.  Second  series.  September  ir 
to  October  6,  1854.  One  division  of  level  =0"  77  from  observations  at  this  station.  One  turn  of 
micrometer  =41"  "420  from  circunipolar  observations  at  this  station. 


Pairs 

3f  sta 

rb. 

Adopted  seconds  of 
mean  N.  P.  D. 

//' 

lU 

L,atitudc. 

V 

" 

// 

0      /         // 

// 

6  052 

6  082 

57  '22 

39-45 

3 

8 

44  12  42-49 

4-0-51 

6  177 

6 

223 

04-82 

40-99 

2 

6 

43-05 

-0  -05 

6  241 

6 

316 

08-99 

36-74 

2 

6 

41  -69 

+  1  -31 

6  395 

*6 

429 

25-72 

14  -28 

4 

7 

42-92 

+0  -08 

*6  429 

6 

522 

14  -28 

58  -88 

5 

7 

42-32 

+0  -68 

6  534 

6 

583 

16-49 

17  -41 

3 

8 

42  -15 

-0  -85 

6  659 

6 

711 

44  -88 

12  92 

6 

12 

42-96 

^0  -04 

6  734 

6 

S06 

54  74 

18  -22 

6 

12 

42-72 

-^0  -28 

6  763 

b 

813 

42-42 

03-10 

6 

12 

43  -62 

—0  -62 

6  .S24 

*6 

915 

51  -20 

37-67 

4 

7 

43  -33 

-0  -33 

*6  915 

6 

928 

37  -67 

52 -Of 

6 

8 

42-73 

+0  -27 

6  940 

7 

024 

31  '54 

19-33 

5 

II 

42  -62 

+0  ■3.S 

7098 

7 

126 

44-25 

36-50 

7 

13 

42  -84 

fo  -16 

7  171 

7 

253 

22-17 

49-23 

7 

13 

43  -02 

—o  -02 

7  278 

*7 

336 

50  -85 

57  -30 

5 

7 

42-76 

+0-24 

7  385 

7 

448 

32-98 

09  -03 

4 

10 

43  -86 

-0  -86 

7  512 

7 

566 

03-20 

58-74 

4 

10 

43-21 

—0  -21 

7  595 

7 

623 

06-75 

16-38 

4 

10 

43-42 

^0  -42 

7  679 

7 

695 

1974 

29-9S 

2 

6 

42-41 

^0  -59 

7  721 

*7 

754 

21  -09 

07  -98 

3 

6 

43-77 

-0-77 

7  731 

*7 

754 

10-96 

07-98 

4 

7 

43-74 

-0-74 

7  894 

*7 

983 

29-04 

34-41 

4 

7 

42  -86 

+  0-14 

7  9'3 

*7 

983 

13  -08 

34-41 

4 

7 

42-45 

+0-55 

-*6  238 

6 

3^1 

46-34 

06  -55 

I 

3 

42-79 

+0-21 

*6  238 

6 

318 

46  -34 

50  -48 

I 

3 

42  -37 

Vo  -63 

6  477 

*6 

571 

52-10 

26-74 

4 

7 

42-66 

+0-34 

6  496 

*6 

57' 

39-21 

26-74 

4 

7 

43-41 

-0-41 

6  687 

6 

722 

30  -87 

38  -90 

6 

12 

42  -60 

+0-40 

6  740 

6 

867 

49  -65 

34  -41 

6 

12 

43-13 

—0-13 

6  926 

6 

975 

33-73 

45-95  ■ 

3 

8 

43  -88 

-0  -88 

6  986 

7 

076 

04  -20 

54-08 

2 

6 

43  •  1 1 

—0  -I  I 

7  "48 

7 

085 

29-07 

13-97 

5 

II 

43  -05 

-0  -05 

7  243 

*7 

336 

29-75 

57-30 

3 

6 

43-21 

—0  -21 

7  782 

7 

843 

25-30 

24-04 

5 

II 

43-52 

—0  -52 

*7  855 

7 

879 

or  -25 

34  -92 

3 

6 

43-15 

-0-15 

•^7  855 

7 

88n 

or  -25 

12-50 

4 

7 

43-04 

—0-04 

II 

idiscriminate 

mean  =  44° 

12'  42 

"  -97. 

V 

/eighted  mean           =  44 

i2    43 

-00  ±L 

y  -05. 

e  =  ±0 

"  -47. 

li 

["]  observations,  36  pairs. 

[Reduction  to  A  = 

= +0^-40.] 

Combination  oj 

'results. 

G.  W.  Dean 

<p  =  44°   12 

'  42" 

92  dz  0" 

-05. 

S.  Harris 

43 

-00   ±  0 

■05. 

Mean 

42 

•96  rt  0 

-04. 

[Reduction  to  A  = 

+  0" 

-40.] 

THE   ASTRONOMIC   MEASURES. 


269 


10.  Salmiliis 

,   M 

iiine.— J 

.  E.  Hilgard. 

Zenith 

telescope  No.    i. 

June  29  to  July 

14,   rS53.     One 

ivision  of  level 

=3 

"'2.     One  turn  of  micrometer 

=45''-52. 

Pairs 

of  stars. 

Adopte<l  seconds  of 
mean  N.  P.  D. 

//  ' 

W 

Latitude. 

V 

// 

// 

0     /         // 

// 

4 

943 

4 

974 

58  -oo 

18  "OO 

4 

4 

44  08  37  -35 

-TO -38 

5 

079 

5 

085 

33  -50 

03-51 

3 

3 

39  26 

-I  -53 

*5 

094 

5 

'52 

34  -30 

32  -30 

2 

2 

39 '30 

-••57 

*5  094 

5 

216 

34  -30 

53-07 

2 

2 

38-92 

-I -19 

5 

168 

5 

177 

55  -40 

57-60 

3 

3 

38  -50 

-0-77 

5 

348 

5 

440 

26  -90 

59-56 

6 

5 

38  -04 

-0-31 

5 

483 

5 

490 

50-25 

29-50 

6 

5 

37-95 

— 0-22 

5 

596 

5 

617 

55  -50 

43-50 

3 

3 

37-54 

+0-19 

5 

592 

5 

621 

37  '60 

44-40 

2 

3 

37  -68 

+0-05 

5 

692 

5 

705 

20  -40 

10-56 

4 

4 

36-96 

+0-77 

5 

714 

5 

734 

01  73 

13 -So 

4 

4 

37  -98 

-0-25 

5 

747 

5 

785 

57-00 

05  -00 

4 

4 

37-64 

+  0-09 

5 

828 

5 

840 

03-60 

26-80 

4 

4 

36-47 

+  1  -26 

5 

900 

5 

972 

26  -00 

18-30 

3 

3 

36-11 

+  1  -62 

5 

922 

5 

978 

30-80 

44-62 

3 

3 

38-24 

-0-51 

5 

991 

6 

047-8 

33  -40 

35 '15 

3 

3 

38  '49 

—0-76 

6  006 

6 

030 

29  -oo 

39-57 

3 

3 

37  -08 

-  0  65 

6 

052 

6 

0S2 

55-50 

37-80 

2 

3 

38 -47 

-0  74 

6 

079 

6 

178 

09-50 

41  -50 

3 

3 

37 -So 

— 007 

6 

237 

6 

289 

25-53 

59-80 

2 

3 

38 -37 

—0-64 

*6 

238 

6 

311 

47-73 

oS  -00 

2 

2 

37-29 

+0-44 

*6 

238 

6 

318 

47-73 

52  -40 

2 

2 

35-83 

+  1  90 

6 

357 

*6 

428 

31  -DO 

55-50 

3 

2 

36-90 

+0-83 

6 

390 

*6 

428 

51  -40 

55-50 

3 

2 

36-90 

+0-S3 

6 

391 

*6 

428 

t8  -20 

55-50 

3 

2 

36 -S3 

-fo-90 

6 

368 

6 

429 

18-50 

18-30 

3 

3 

38-45 

-0-72 

6 

453 

6 

586 

16-60 

02  -00 

I 

I 

37-13 

4-0  60 

6  4S0 

6 

522 

01  -03 

04  -00 

4 

4 

38-55 

-0  -82 

6  5S2 

6 

612 

'8 -35 

49  -40 

4 

4 

38  -02 

—0-29 

6 

625 

6 

644 

14-50 

57-00 

4 

4 

37  -47 

-fo-26 

6 

667 

6 

687 

25  -20 

38  -60 

4 

4 

37-81 

— 008 

6 

737 

6 

758 

32  -02 

38  -84 

4 

4 

37  -23 

-1-0-50 

6 

783 

6 

836 

31   20 

24-30 

2 

3 

36-79 

-ro-94 

6 

S35 

6 

905 

45  -36 

24  -50 

4 

4 

38-27 

-0-54 

6  S56 

6 

937 

57  -60 

25  -50 

' 

1 

38-24 

-0-51 

Indiscriminat 

e  mt'an  = 

44°  08'  37'^ 

■71- 

Wei<;lite(l  me 

Ul             = 

44    oS    37 
*o"-77. 

•73±o 

"•09. 

1 10  observations,  35  pairs. 

[Reduction  toA=— o"-i5.] 


270 


THE    EASTERN    ORLIOUE    ARC. 


II.  Rloant  Pleasant,  Maine. — G.  W.  Dean.  Zenith  telescope  No.  5.  July  20  to  August  19,  1S51. 
One  division  of  level  =  i""58  from  observations  at  this  station.  One  turn  of  micrometer  =  4i'''4oo 
from  circumpolar  observations  at  this  station  and  Cape  Small,  Maine. 


Pairs  ( 

jf  stars. 

54S4 

5  502 

5  497 

5  552 

5  602 

5  717 

5  604 

'■5  629 

*5  629 

5  693 

5  ''i4o 

5  860 

5  922 

5  97S 

5  9S6 

6  079 

6  129 

6  268 

6  178 

6  216 

6  238 

6  318 

*6  255 

6  349 

*6  255 

6  355 

6  390 

*6  42S 

6  391 

*6  428 

6  530 

6  556 

6  566 

*6  599 

*6  599 

6  659 

6  667 

6  687 

6  712 

6  740 

t2    872 

6  784 

6  763 

-6  849 

*6  849 

6  895 

6  915 

6  928 

6  932 

6  940 

6  943 

6  970 

7  008 

7  062 

7  022 

7  076 

*7  09S 

7   "7 

*7  098 

7   126 

7  171 

7  333 

7  243 

7  336 

7  385 

7  448 

7  398 

7  411 

7  636 

7  721 

7  643 

7  73' 

7  679 

*7  800 

*7  800 

7  850 

7  843 

■  7  871 

7  894 

7  948 

Adopted  seconds  of 
mean  N.  P.  D. 

n' 

w 

Latitude. 

ij 

// 

// 

0      /         // 

// 

58-15 

16  -00 

4 

12 

44  01  36  -53 

— 0  -09 

03-20 

10  -80 

I 

7 

36-65 

-0-21 

33-12 

53-44 

3 

II 

36-06 

+0-3^ 

2770 

03-72 

5 

9 

35-96 

+  0-48 

03-72 

55-16 

5 

9 

35-92 

+0-52 

18-15 

55  -68 

6 

14 

35 -60 

+0-84 

24-62 

38  -73 

6 

^4 

36-67 

-0-23 

56-15 

oS  -36 

6 

14 

36  -59 

-0-15 

25-98 

14-90 

5 

13 

37  -2^ 

-0-84 

43-15 

40-77 

6 

14 

35-93 

+  0-51 

50-51 

56-89 

4 

12 

36-43 

+0-01 

05  -32 

25  -76 

5 

9 

35-77 

+0-67 

05  -32 

07-90 

6 

9 

35  -98 

+0-46 

58  -25 

03-50 

5 

9 

36-67 

-0-23 

24-80 

03  -50 

6 

9 

36-10 

+0-34 

12  -40 

49  '59 

6 

14 

36-92 

-0-48 

27-50 

44-18 

6 

9 

36-32 

+0-12 

44-18 

05-21 

5 

9 

35-95 

+0-49 

39-76 

52-67 

6 

14 

37-23 

-0-79 

52-92 

13  -38 

6 

14 

36  ^i 

-0-47 

29-34 

58-94 

6 

14 

36-12 

+0  -32 

07  -06 

23-50 

5 

9 

36-91 

-0-47 

23  "50 

28-56 

6 

9 

36-44 

0-00 

06  -50 

25-13 

5 

13 

35-74 

40-70 

09-68 

03-80 

6 

14 

36  -68 

—0  -24 

55-73 

18-08 

6 

14 

36-48 

—0-04 

51  -78 

32  -16 

6 

14 

36-31 

-I0-13 

04-05 

28  -67 

6 

14 

36-7' 

-0  -27 

20  -23 

52-21 

5 

9 

36  -45 

—0  -01 

20  -23 

13  -46 

6 

9 

36  -80 

—0-36 

00-03 

52-15 

6 

14 

36-41 

-f  0  -03 

09-67 

49  -65 

6 

14 

36-99 

-0-55 

1 8  -69 

54  -90 

6 

14 

,     36-71 

--0-27 

40-13 

05  -86 

6 

14 

35  -63 

+0-81 

19-39 

13  79 

6 

14 

36-12 

+0-32 

35-07 

04  -28 

5 

13 

36-75 

-0-31 

II  -41 

44-47 

5 

9 

36-44 

0-00 

44-47 

20-58 

6 

9 

36-23 

+0-21 

16  -83 

41  -58 

6 

14 

36-15 

+0-29 

25  "oi 

17-65 

6 

14 

36  -43 

+0  -01 

tOroonibi 

■idge. 

THK    ASTRONOMIC    MEASURES. 


27J 


II.   Mouiil  Pleasant,  Maine — continued. 


Pairs  of  stars. 


7  901 
8058 

8  171 
8  229 


t3  901 
8  076 
8  224 
8  261 


Adopted  seconds  of 
mean  N.  P.  D. 

n' 

lU 

Latitude. 

V 

// 

// 

0 

/ 

// 

// 

26-44 

39  -^'^ 

6 

14 

44 

01 

.36-51 

—0-07 

00  -(XJ 

19 '65 

6 

'4 

36 -to 

-0-36 

27  -40 

55  -36 

5 

13 

36-46 

-0  -02 

22  70 

24  'OO 

2 

10 

36-80 

—0-36 

Iiuliscriniinate  mean 
Weiglited  mean 


I 


:44°  01'  36"-42. 
:  44     01    36    ■44dro"-o4. 
e  —  ±:  o"-30. 
236  observations,  44  pairs. 

[Reduction  to  A  =  +  0^-05.] 

12.  Cape  Small,  Ma\n&. — G.  W.  Dean.  Zenith  telescope.  September  17  to  October 
division  of  level  =1^-598  from  observations  at  this  station.  One  turn  of  micrometer  = 
circumpolar  observations  at  this  station. 


10,  1 85 1.     One 
=  4 1 "'429  from 


I 


Pairs  of  stars. 

Aciopieu  se 
mean  N. 

conas  01 
P.  D 

n' 

7V 

Latitude. 

7' 

// 

// 

0      /         // 

// 

6  497 

6 

522 

35-57 

13  -96 

6 

18 

43  46  43-13 

+  0-56 

6  571 

6 

583 

43-98 

35  -34 

6 

18 

43-72 

-003 

6  599 

6 

659 

44-20 

05-20 

6 

iS 

43 -48 

-f-0-2I 

6  667 

6 

697 

40-00 

09  -20 

6 

iS 

44-32 

-0-63 

6673 

6 

712 

01  -34 

55  -24 

6 

18 

43-26 

+0-43 

6  745 

6 

754 

24-42 

33  -70 

7 

18 

43-63 

+o-o6 

6  849 

6 

895 

23  55 

28  -55 

6 

18 

44-29 

— o-6o 

6  851 

6 

928 

35  -46 

23  -13 

7 

18 

43-24 

+0-45 

6  932 

6 

943 

09  -65 

56  -30 

6 

i8 

43-75 

— o-o6 

69S3 

6 

996 

29-56 

48-50 

7 

18 

43-20 

+0-49 

7  008 

7 

076 

52  -45 

28-65 

7 

18 

43  69 

o-oo 

7  024 

7 

126 

53  -63 

13  -46 

6 

18 

43-30 

+0-39 

7  100 

7 

171 

50  -48 

00-I2 

7 

18 

44-26 

-0-57 

7  204 

7 

262 

07-46 

II  -69 

6 

18 

43 -oS 

+0-6I 

7  277 

7 

301 

15-44 

31  -lo 

6 

18 

44  26 

-0-57 

7  317 

7 

333 

42-19 

52-26 

5 

18 

43-32 

+0-37 

7  345 

7 

383 

54-64 

10  -06 

6 

18 

43-60 

4-0-09 

7  39S 

7 

411 

40  -36 

05  -70 

6 

iS 

43  -42 

+0-27 

7  448 

7 

462 

54  ■9« 

43  -25 

6 

18 

43  -96 

-0-27 

7  503 

7 

544 

54  -30 

02  -48 

6 

iS 

43  -98 

—  0  -29 

7  582 

7 

607 

07-09 

03  -56 

6 

18 

43  -79 

— 010 

7  598 

7 

614 

42  -oo 

33-81 

6 

iS 

43  -53 

+o-i6 

7  731 

7 

813 

04  -22 

22  -40 

6 

18 

43-03 

+0-66 

7  843 

7 

87 1 

16  -70 

41  -60 

6 

iS 

44-17 

-0-4S 

7  803 

7 

S94 

'4  -73 

24-76 

6 

18 

45-77 

— o-oS 

7  8S2 

7 

901 

58 -92 

26-46 

6 

18 

43  -50 

+019 

7  906 

7 

983 

01  -18 

31  -20 

6 

iS 

43-99 

—0  -30 

8  028 

8 

058 

33  -27 

59  -8o 

6 

iS 

43  99 

—0-30 

t3  952 

*8 

076 

24-35 

1 8  -88 

6 

12 

43  -53 

-fo-i6 

t  r.  room 

iridge. 

272 


THE    EASTERN    OBLIQUE    ARC. 


12.   Cape  Siiiall,  Maine — continued. 


Pairs  of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

)i' 

7V 

Latitude. 

V 

// 

// 

0 

/ 

// 

// 

*S  076 

8 

115 

18-88 

26  -85 

6 

12 

43 

46 

4376 

—0-07 

8  1 14 

8 

212 

53 '60 

04  -50 

6 

1 8 

43 '99 

-0-30 

8   171 

8 

261 

27  -40 

24  -28 

6 

18 

43 '91 

—0  -22 

iSo 

259 

20  '60 

35  '44 

6 

18 

43  '^1 

-0-18 

330 

337 

15-12 

43  '42 

6 

18 

43  •S5 

-  0  •  1 6 

4S7 

502 

43 '50 

46  -84 

6 

18 

43  ■'''O 

—0  -I  I 

649 

673 

01  -28 

47-40 

.      6 

18 

43  "15 

1  n  '54 

706 

727 

3«  -S'^ 

58 -10 

6 

18 

43  "95 

—0-26 

,si9 

877 

49-66 

22  -98 

5 

18 

43  '63 

-|-o  -06 

915 

947 

04  -20 

53  '30 

6 

18 

4371 

—0  -02 

953 

1 

043 

nd 

27-56 
iscriniinate 

25  -90 
mean 

6 
=  43°  46' 

43 

r8 
''-69. 

43 '91 

—0  -22 

\ 

Vei 

ghted  mean 

=  43    46 

43 

•69 

d=0 

04. 

t 

=  zbo"-2 

3- 

243  observations,  40  pairs. 

[Reduction  to  A  =  —  o"-2i.] 

13.  Mount  Independence,  Maine. ^A.  D.  Bache  and  G.  Davidson.     Zenith  sector  No.  i.     Fir.st  series. 
September  21  to  October  27,  1849.     Mean  value  of  one  division  of  level  =  o"-72i.      (Levels  No.  3.) 


St 

irs  north  of  zenith. 

stars 

soutl 

of  zenith. 

Stars. 

Adopted 
seconds 
of  mean 
N.  P.  D. 

n' 

Latitude. 

V 

Stars. 

Adopted 
seconds 
of  mean 
N.  P.  D. 

it' 

Latitude. 

V 

// 

0        /           // 

// 

r' 

0         /           // 

// 

16 

06  'OO 

4 

43    45     35-22 

— 0-2I 

58 

07-46 

4 

43     45     34  -02 

+0-14 

169 

30-02 

5 

34-84 

+  0-17 

100 

28-50 

4 

35  -58 

-1  -42 

180 

00  -20 

4 

34-78 

+  0-23 

259 

14  -80 

4 

34-99 

-0  -83 

330 

53 -So 

4 

35-23 

—0  -22 

337 

22  -00 

3 

34-88 

-0-72 

474 

02  -30 

I 

34-78 

+0-23 

502 

23-60 

3 

34-53 

-0  -37 

487 

20  -50 

3. 

35-16 

-0-15 

649 

36-00 

3 

32-98 

+  1  -18 

673 

21  -50 

3 

34-03 

+  O-9.S 

727 

3' -48 

3 

33-95 

+  0  -21 

706 

1 2  -40 

3 

35-76 

-0-75 

877 

54-20 

4 

35-02 

-0-86 

819 

21    20 

4 

34-05 

+  0-96 

915 

33  -70 

3 

34-19 

—0  -03 

947 

22  -40 

3 

35  -84 

-0-83 

953 

56-30 

3 

33-98 

+o-i8 

I  043 

52-44 

6 

35-19 

-0-18 

2  485 

09-18 

3 

33-56 

-|-o  -60 

3  048 

10-77 

4 

35  -42 

—  0-41 

6  355 

14  -10 

8 

34-29 

■0-13 

5  937 

'   05-30 

4 

35  -83 

-  0-82 

6  429 

33-71 

6 

34-40 

—0  -24 

6  091 

28  -90 

8 

35-15 

—  0  -14 

6  497 

45  -01 

4 

33  -26 

+0-90 

6  522 

23  -84 

I 

34-20 

-f  o-8i 

6  571 

55-50 

4 

32-60 

+ 1  -56 

6  583 

47  '3" 

3 

36-62 

-I  -61 

6  673 

15-30 

2 

34-04 

-|-0  -12 

6  712 

08  -lo 

4 

36  -32 

-i  -3' 

6  745 

40-70 

4 

35-27 

—  I  -11 

6  754 

50  -06 

3 

34-55 

+  0-46 

6  784 

15  -26 

4 

33-29 

+  0-87 

6  928 

45-54 

4 

33-32 

+  1-69 

6  851 

54-00 

4 

33-62 

+0-54 

6  983 

51  -30 

4 

33-84 

+  I-I7 

6  996 

10  -60 

3 

33-94 

+  0  -22 

7  076 

52-10 

4 

35-70 

—0  -69 

7  ooS 

14-72 

4 

32-69 

+  1  -47 

THE    ASTRONOMIC    MKASURKS. 


273 


13.   Mount  Independence,  Maine.     I^'irst  series— coiiliiiucil. 


Stars. 


7   171 

7  262 

7  3"' 

7  3'7 

7  345 

7  411 

7  44H 

7  503 

7  S'^^z 

7  598 

7  643 

7  7^2 

7  «'3 

7  S71 

7  882 

7  894 

7  9S3 

S  05  s 

8    115 

8  26  r 

8  310 

.stars  iiortli 
Adopted 
.seconds         , 
ofiiieaii      " 
N.  I'.  U. 

of  zenith. 
Latitude. 

// 

0      /         // 

25  '40 

7 

43  45  33  '84 

38  '68 

3 

34-81 

58  -80 

4 

36-12 

10 -18 

2 

33-56 

23-20 

2 

34-04 

35  -So 

3 

33-60 

25 '50 

4 

36-24 

25  75 

5 

35  -82 

39  '85 

3 

35-73 

15 '40 

4 

34-74 

08  -81 

6 

35-42 

54-00 

2 

37-07 

58  -oo 

4 

34-18 

18-50 

5 

33  -07 

35 '96 

3 

35-52 

01  -80 

4 

36-01 

09-40 

3 

35-17 

38  -50 

5 

36-50 

06  '04 

4 

33-86 

04  -20 

4 

34-99 

26  -40 

4 

34-46 

+  1 

-'7 

-to 

-20 

—  I 

■I  I 

+  1 

•45 

+0 

-97 

+  1 

■41 

—  1 

■23 

— 0 

•81 

-0 

•72 

+0 

■27 

— 0 

■41 

—  2 

•06 

+0 

•83 

+  1 

■94 

— 0 

-51 

—  I 

-00 

— 0 

■16 

—  I 

■49 

+  1 

-15 

+0 

-02 

+0 

•55 

7    ICXJ 

7  204 

7  277 

7  333 

7  336 

7  368 

7  383 

7  398 

7  462 

7  544 

7  607 

7  614 

7  73' 

7  S03 

7  S43 

7  9"! 

7  948 

8  028 

8  076 

8  171 

8  229 

Stars 

■icnith 

of  zenitli 

Adojjtcd 

seconds 
of  mean 

»' 

I.ati 

nde. 

V 

N.  I>.  D. 

// 

0      / 

// 

// 

14-58 

3 

43  45 

34  -88 

—0  72 

34-00 

4 

32  -91 

^- 1    25 

42  -So 

4 

34  75 

-0-59 

20  -60 

3 

34  3' 

-0-15 

24  56 

4 

34-47 

-0-31 

23  -80 

5 

34-05 

-)-o-ii 

39  40 

3 

32  -82 

-  I  -34 

10  TO 

4 

36 -68 

-2  52 

14  -lo 

4 

34  46 

—0-30 

34  -80 

4 

33-57 

-t"0-59 

36  -70 

4 

33-91 

+0-25 

07  -16 

3 

33-28 

+0  -88 

39  '2o 

4 

34-37 

-021 

.5"  '75 

3 

33  -04 

^i  -12 

53  '.so 

2 

35  ■ '  5 

-0  -99 

03  '73 

4 

33  99 

+0-17 

55  -31 

3 

34  78 

—0-62 

1  1  -.85 

5 

34  71 

-0-55 

58  -20 

3 

33  67 

-1-0-49 

06-95 

4 

35  -07 

—0  -91 

02-57 

4 

34  -88 

-0-72 

160  observations,  42  .stars. 
%  =  43°  45'  35"-oi. 

<P=>^('P„+<PJ=43°  45'  34"-58±o"-o7 


157  observations,  42  .stars. 
%=43°  45'  34"- 16. 


13.  Rfonnt  Independence,  Maine. — G.  W.  Dean.     Zenith   telescope  No.  2.     Second  series.     Sep- 
tember 20  to  October  20,  1849.     One  division  of  level  =0^-90  from  observations  at  this  .station.     One 

turn  (if  micrometer  =44^-880  from  the  latittide  observations  at  this  .station. 


I'airs  of  stars. 


6  368 
6  497 
6  57' 
6  673 
6  745 

6  85 1 
6983 

7  008 
7  100 
7  204 
7  277 
4192 


6  427 
6  522 

6583 
6  712 

6  754 
6  928 

6  996 

7  "76 
7  "71 
7  262 

7  301 
—No.  7- 


-02- 


Adopted  seconds  of 
mean  N.  P.  D. 

// 

// 

32  -92 

13  94 

45  -oi 

23  -84 

55-50 

47-30 

15-30 

oS  -lo 

40  -70 

50  -06 

54-00 

45-54 

5'   30 

10  60 

14-72 

52-10 

14-58 

25  -40 

34.  CXI 

;vS  -68 

42  -80 

58  -80 

-18 

-M 

Latitude. 

V 

0       /        // 

// 

2 

43  45  33  -67 

-(-0-66 

5 

33  48 

+  0-85 

5 

34  -28 

^0-05 

5 

34  83 

—0-50 

6 

34  -49 

— o-i6 

6 

33  -45 

-fo-SS 

5 

33  25 

+  t  -oS 

5 

33  - 1 ' 

•    I  -22 

6 

34  80 

-0  -47 

5 

33  -82 

-^0-51 

5 

34  65 

-032 

' 


274 


THE    EASTERN    OBLIQUE    ARC. 


13.   Mount  Iudepcndena\  Maine. 

Second 

series 

—continued. 

Pairs  of 

stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

n' 

u. 

Latit\ule. 

V 

// 

// 

Of// 

// 

7  317 

7 

333 

iotS 

20 -60 

5 

6 

43  45  34  -oi 

+0-32 

7  345 

7 

3S3 

23  '20 

39-40 

4 

5 

33  -82 

+0-51 

7  448 

7 

462 

25  '50 

14  TO 

4 

5 

33-74 

+0-59 

7  503 

7 

544 

2575 

34  -So 

4 

5 

33  -92 

+0-41 

7  582 

7 

607 

39  '85 

36  -70 

4 

5 

33  -85 

-\-o  -48 

7  731 

7 

813 

39-20 

58-00 

5 

6 

33  -32 

+  1  -OI 

7  843 

7 

871 

53 '50 

18-50 

4 

5 

34-16 

+0-17 

7  S82 

7 

901 

35 '96 

03  -73 

4 

5 

33  -79 

+0-54 

8  028 

8 

05S 

11-85 

38  -50 

5 

6 

34  -35 

—0  -02 

S  076 

8 

115 

58  "20 

06  -04 

4 

5 

35-19 

—0  -86 

8  171 

8 

261 

06-95 

04  -20 

4 

5 

34-3' 

+  0-02 

180 

259 

00 -20 

14  -80 

3 

5 

34  -27 

+0  -06 

330 

337 

53  -So 

22  -00 

3 

5 

34  -30 

+0-03 

7  398 

7 

411 

10  -lo 

35  -So 

6 

6 

34  -97 

—0-64 

7  598 

7 

614 

15  -40 

07-16 

7 

6 

34  -70 

-0-37 

7  S03 

7 

S94 

50-75 

01  -80 

6 

6 

35  -32 

-0  -99 

487 

502 

20-50 

23  -60 

6 

6 

35  -64 

-I  -31 

649 

673 

36  -GO 

21  -50 

6 

6 

34  -70 

-0-37 

706 

727 

12  -40 

31  -48 

5 

6 

35-28 

-0-95 

819 

S77 

21  -20 

54  -20 

6 

6 

34  -66 

-0-33 

915 

947 

33  -70 

22  -40 

6 

6 

35-14 

-o-8[ 

953 

I 

043 

56  -30 

52  -44 

6 

6 

34  -37 

—0  -04 

lilting  latitude  by  coi 

Indiscriminate  mean  =  43' 

Weighted  mean            =  43 

e  =  ±. 

151  observations,  33  pairs. 

[Reduction  to  A  =  — 

nhination  of  scries            =43' 

'45'34 
45  34 
o''-52 

3" -03 
'45 '34 

''•29. 
'33 

■] 
"•47 

±o"-oS. 
±o"-o6. 

14.  Gunstock,  New  Hampshire. — J.  H.  Toomer.  Zenith  telescope  No.  5.  July  i 
i860.  One  division  of  level  =  o"-94S  from  observations  at  this  station.  One  turn 
—  4i''-39i  from  circunipolar  observations  at  this  station. 

Adopted  seconds  of 
mean  N.  P.  D. 


I  to  August  9, 
of  micrometer 


Pairs 

of  stars. 

5  400 

5  417 

5   479 

5   499 

5  541 

5  599 

5  629 

*5  731 

5  658 

*5  731 

5  785 

5  863 

5  918 

5  93' 

6  079 

6  087 

*6  147 

6  184 

*6  147 

6  216 

18  -63 
09-30 
17-84 
05-31 
27-34 

40  -02 

48  -28 
15-06 

20  -29 
20  -29 


53-62 
24-77 

35  -36 
53  -90 
53  -90 
58-20 

19  -58 
48  -6r 
50  -90 
3'  -23 


n' 

7V 

Latitnde. 

V 

0      /         // 

// 

8 

14 

43  31  03-24 

+0-57 

7 

14 

03-24 

+0-57 

9 

15 

03-25 

+0-56 

7 

9 

03  -67 

+0-14 

8 

10 

03-50 

+0-31 

8 

14 

03-76 

+0-05 

8 

14 

04-14 

-0-33 

8 

14 

03  -22 

+0-59 

7 

9 

03-15 

+0-66 

7 

9 

03-41 

+0-40 

THE    ASTRONOMIC    MEASURES. 


27 


/D 


Pairs  of  stars. 


f 


*6  235 
*6  235 
6  365 
6  456 
6  493 
6  599 
6  648 

6  734 
*6  861 
*6  861 
*6  983 
*6  983 

7  064 
7  105 
7  174 
7  297 
5  643 

*5  666 
5  788 
5  853 

5  911 

6  095 
6  231 
6  251 
6  392 
6  495 
6  542 
6  656 

*6  720 

6  745 
6  824 
6  8S1 

6  962 

7  027 
7  158 
7  241 
7  253 


6  246 

6  258 

6  428 

6  470 

6  520 

6  626 

6  681 

6  771 

6  940 

6  943 

7  022 
7  048 

*7  132 
*7  132 
7  233 
7  345 
-5  666 
5  752 
5  795 
5  886 

5  929 

6  162 
*6  316 
*6  316 

6  421 
6  516 
6  629 
*6  720 
6  728 
6  779 
6  851 
6  915 

6  996 

7  112 
7  198 

*7  333 
*7  333 


14.   Gimslock,  New  Hampshire-  — coiilinucd. 


43 


dopted  seconds  of 
iiieaii  N.  P.  D. 

;/' 

a. 

// 

>/ 

4672 

43-73 

8 

10 

4672 

55-44 

8 

10 

39 '25 

28  -7,S 

7 

14 

"3  76 

52  -24 

7 

14 

40  -5 ' 

42-42 

7 

14 

49-11 

18  -76 

S 

14 

59  -50 

14-64 

8 

14 

06  'lo 

54-19 

7 

14 

48  -55 

29-95 

7 

9 

48  '55 

21  -80 

7 

9 

52  "OO    . 

22-25 

7 

9 

52  -OO 

19-67 

7 

9 

18-51 

49-71 

7 

9 

39 '91 

49-71 

7 

9 

58-31 

13-31 

7 

14 

38  '90 

45-46 

7 

14 

00-85 

07  -58 

3 

6 

07-58 

17-49 

4 

7 

50-44 

42-70 

8 

14 

27-70 

22  'OO 

8 

14 

14-74 

39-71 

7 

14 

08  -63 

13-31 

6 

13 

42-56 

23-72 

8 

10 

26-59 

23  -72 

9 

10 

20  -43 

18-35 

7 

14 

27  -38 

44-53 

6 

'3 

48-49 

49-29 

6 

13 

58-16 

38  -07 

6 

S 

38-07 

20-67 

6 

S 

n  -43 

33  -02 

6 

13 

57  -28 

11-96 

7 

14 

36  -89 

40  -oS 

8 

14 

22  -23 

09  -68 

7 

14 

11  -21 

06  -95 

7 

14 

49-66 

35  -97 

7 

14 

59  -45 

44  -63 

7 

9 

28  -64 

44  -63 

7 

9 

I^alitude. 

V 

/          // 

// 

3 '  "3  -90 

— 0'09 

03  -87 

— o-o6 

03-95 

-OT4 

04  -21 

—0-40 

03  -74 

-f-o  -07 

03-62 

+0-19 

03-70 

—  Q-II 

03-73 

-rO-08 

03-80 

.  -^o•oI 

04  ■2\ 

—0-40 

04-23 

—0  -42 

04-09 

—0  -28 

93  -88 

—0-07 

04-73 

—0  -92 

04  -2r 

—0-40 

04-05 

—0-24 

03-72 

—0  -09 

03 -84 

—0-03 

04  -21 

—0  -40 

03-75 

-f  0  -06 

03-47 

-0-34 

04-45 

—0  64 

04-15 

-0-34 

04-27 

—0-46 

04  -01 

—0-20 

03  -58 

-0-23 

03  -09 

-fo-72 

03-92 

— o-ii 

03-21 

—0  '60 

04  -48 

—0-67 

04  -21 

—0-40 

03  -58 

-0-23 

03-90 

--0  09 

04-31 

—0-50 

03  -oS 

-0-73 

04-04 

-0-23 

04-51 

—070 

Indiscriiiiinale  mean  =43°  31'  03'"-84. 
Weighted  mean  =43    31    03     -8iiho"-o5. 

<»==to"-5o. 
333  observations,  47  pairs. 

[Reduction  to  A=-f-i"-33-] 


276 


THE   EASTERN   OBLIQUE   ARC. 


15.  Agamenticus,  Maine. — T.  J.  Lee.  Zenith  telescope  Military  Academj'.  First  series.  Sep- 
tember 15  to  October  10,  1847.  One  division  of  level  =  i^^"28.  One  turn  of  micrometer  =  44"79i 
from  latitude  observations  at  this  station. 


Pairs 

3f  stars. 

6  5S2 

6  662 

6  735 

6  744 

6  75« 

6  834 

7  377 

-■•7  461 

7  387 

*7  461 

*7  533 

*7  571 

■"7  533 

*7  5«4 

*7  533 

n  586 

*7  542 

'•■■7  571 

*7  542 

*7  584 

*7  542 

*7  5S6 

7  607 

7  668 

7  693 

7  718 

7  755 

7  798 

7  '^29 

7  958 

*7  997 

-<-8  039 

*7  997 

-■••■8  077 

*8  146 

*8  039 

*S  146 

•<-8  077 

*8  256 

8   188 

*S  256 

8  268 

S  374 

*7 

4 

*7 

32 

68 

164 

182 

253 

395 

412 

430 

Adopted  seconds  of                   , 
mean  N.  P.  D. 

w 

Latitude. 

-. 

// 

// 

0      /        // 

// 

54 '24 

47  -oo              3 

2 

43  13  25  -79 

—0  -84 

56  -90 

28  -90              .5 

3 

25  -06 

^0  -II 

26  63 

00  -50              4 

3 

23  -Si 

+  1  -14 

28  •  1 6 

18-13              5 

2 

26-16 

—  I   -2] 

55  ■«4 

18-13              5 

2 

26  -21 

-I  -26 

J  8  '00 

19-17              5 

25-76 

-0-81 

18  -oo 

10  -37              4 

24-03 

+  0-92 

I  8  'GO 

31  -50              5 

25  -70 

-0-75 

25  '30 

19-17              4 

24  -62 

+  0-33 

25 '30 

10-37              3 

23-07 

+  1  -88 

25  '30 

31  -50              4 

24-70 

+0-25 

10  '00 

21  -80              5 

3 

25  -09 

—0  -14 

36  '97 

16-70              5 

3 

25-24 

—0  -29 

1970 

17-07              6 

4 

24-88 

+0-07 

56-32 

1 8  ■(:»               6 

4 

25-56 

—0  -61 

00  '80 

54  -20               5 

2 

24  -60 

+0-35 

00  'So 

17-60               5 

2 

24-93 

+0  -02 

31  74 

54  -20               5 

2 

24-41 

+0-54 

3>74 

1 7  -60               5 

2 

24-74 

+0  -21 

08  -48 

38  -90               7 

3 

24-25 

+0-70 

08-48 

00  -32               7 

3 

24-73 

-|-o  -22 

20  -87 

39  -60              2 

I 

25  -oo 

-  0  -05 

J5-67 

39-60              3 

2 

22  -78 

+  2-17 

39  -66 

33  '26              4 

3 

25 -oS 

-0-13 

II  -90 

II  -13              4 

3 

26-18 

-I   23 

47-50 

31  -04              2 

2 

25-50 

-0  -55 

15 '52 

30  -52              3 

2 

24-43 

+0-52 

Luliscriminate  mean  =  43° 

13'  24'' 

•90. 

Weighted 

mean           =  43 

13     24 

-95  =t  o'^"io. 

f  =  =b  o''-99. 

121  observations,  27  pairs. 

[Reduction  to  A  =  — 

o^'-ii.] 

15.  Aganienticus,  Maine.— A.  D.  Bache,  R.  H.  Fauntleroy,  C.  O.  Boutelle.     Zenith  sector  No.  i. 
Second  series.     October  4  to  November  15,  1S47.     Mean  value  of  one  division  of  level  =o"'-]2-]. 


Stars. 

7  277 
7  39S 
7  462 
7  731 


stars  north 

of  zenith. 

stars. 

.Adopted 
seconds 

of  mean. 
N.  P.  D. 

11' 

Latitude. 

t) 

// 

0      /         // 

// 

7  091 

38  -ID 

I 

43    13   25-78 

-0-23 

7  171 

50-60 

5 

25  -42 

-i-O-13 

7  345 

51  -60 

5 

25  -72 

-0-17 

7  560 

24  -60 

6 

26-55 

—  I  -00 

Stars  south 

of  zenith. 

Adopted 
seconds 

of  mean. 
N.  P.  D. 

«' 

Latitude. 

V 

// 

0      /         // 

// 

09  -90 

5 

43  13  25-47 

—  0-70 

39-75 

4 

24  -89 

-  012 

44-90 

5 

24   26 

+0-51 

14-50 

3 

24-45 

+  0-32 

THE    ASTRONOMIC    MEASURES. 


27; 


15.     /Ifrainciiticiis,  Maine.     Second  series — continue'l. 


Stars. 

Stars  nortli  0 
Adopted 
seconds          , 
of  mean        " 
N.I'.  I). 

r  zenith 

I.atitnde. 

7J 

stars. 

stars  sonth 
Adopted 
seconds          , 
of  mean        ' 

N,  I'.  O. 

of  zenith 

I.atitnde 

// 

0       /        // 

f  f 

// 

0      /         // 

7  705 

41  -17 

2 

43   '3  24-88 

\    0  -67 

7  777 

41   -80         2 

43   13  24  48 

7  S15 

1 0  "06 

2 

26  -93 

.-38 

7  H50 

34  -«)      3 

25-65 

7  888 

36-40 

2 

27-46 

1    -91 

7  972 

58  -60      3 

24  -89 

7  906 

15-90 

4 

25  -04 

+  "-51 

7  994 

4 1 ■ 00       1 

25-25 

8  036 

42-56 

3 

26-34 

-0-79 

8  136 

07  -52       4 

24-30 

8  107 

39  '28 

2 

23-72 

+  I-S3 

8  345 

05  -26       2 

24-71 

8  224 

13  '20 

2 

25-35 

-j-u  -20 

58 

47  -6<-'       3 

23-17 

8  231 

30  -50 

4 

27  -05 

-1  -50 

480 

43  -20      3 

24-96 

8  289 

40  -30 

4 

24-21 

4  I  -34 

566 

40  -50       3 

24  69 

16 

45  75 

3 

2371 

-f  I  -84 

656 

22  -GO       3 

25-13 

100 

07-90 

5 

25-52 

4  0  -03 

821 

24  -20       2 

25  63 

180 

39  '2o 

2 

26-61 

—  I  -06 

912 

13  -48       2 

24  46 

330 

32  -48 

I 

24-32 

+  1-23 

981 

26  -90       r 

2\  -6S 

404 

29  -28 

2 

25  -H6 

-0-31 

735 

03-30 

I 

25  -06 

4  0  -49 

<P„  =  43°   13' 
56  observations 

25"  -55- 
>,  19  stars. 

[Reduction 

<?»„  =  43 
49  observ 
=  43=   13'  25"  -i6±o"-ii. 
to  A  =  -o"-ii.] 

°   13'  24"  -77. 
ations,  17  stars. 

+0-29 

-o  -88 
-012 
-o  -48 

-i  0-47 
-f-o  -06 
4-1  -60 
-()  -19 
-|-o  -08 
—0-36 
-0-S6 
^0-31 
-to  09 


15.   Agaiiwnticus,  Maine. — A.  D.  Bache,  R.  H.  Fauntleroy,  G.  Davidson.     Transit  No.  2  in  prime  ver- 
tical.    Third  series.     October  18  to  November  26,  1847. 


43 


Stars. 

Adopted 
seconds 
of  mean 
N.  P.  D. 

// 

n' 

2t, 

6  355 

20  -24 

4 

4 

7  022 

49-40 

4 

4 

8  023 

42-25 

4 

4 

60 

32  -05 

2 

2 

7  972 

58  -72 

2 

2 

8  229 

42-18 

2 

2 

963 

I  7  -40 

I 

I 

I  320 

02  -25 

I 

I 

1  398 

08  -00 

I 

I 

Latitvide. 

V 

/           // 

// 

13   24  -92 

-^0-05 

24-67 

-rO-30 

24-65 

+  0-32 

25  -53 

—  0-56 

24  -06 

-to -91 

25  -33 

-0  -36 

25  -27 

-0-30 

25  -65 

—  0  -6S 

26  -72 

-I  '75 

'    25"-(K). 

24     -97  ±: 

o"-i4 

Indiscriminate  mean  =  43°    13 
Weighted  mean  =43     13 

e  =  rto"-44. 
21  ob.servations,  9  .stars. 

[Reduction  to  A  =  C'-qo.  ] 

Combination  of  results  for  latitude  referred  to  A- 
By  zenith  telescope  43°   13'   24"-84  :=  o"-io. 

By  zenith  sector  43     13     25     05—0     11. 

By  transit  in  prime  vertical       43     13     24    '<y;  ^o     14. 
Weighted  moan  43      13     24    -96:^0    -06. 


278 


THE    EASTERN    OBLIQUE    ARC. 


16.   /.s7('.s- (7/\S"/'t)(7A-,  Maine. — T.J.Lee.     Zenith   telescope  Militar}-   Academj'.     August   4   to  22, 
1847.     One  division  of  level  =  t''-2S3.     One  turn  of  micrometer  =  44'''962. 


Pairs  of  stars. 


*6  079 

*6  079 

*6  079 

*6  34S 

*6  348 

*6  34S 

6  547 

6  642 

6  647 

6  762 
*6  8S2 
*6  882 
*6  8S3 
*6  883 
*6  979 
*6  979 

7  013 
7  105 
7  188 
7  281 
7  474 


*6  150 
-6  234 
*6  238 
-6  150 
™6  234 
*6  23S 
6  601 
*6  735 
*6  735 

6  81S 
*6  932 
*6  970 
*6  932 
-6  970 
-6  932 
%  970 

7  024 
7  152 
7  220 
7  368 
7  658 


Adopted 
mean 

seconds  of 
N.  P.  D. 

// 

// 

05  -35 

16-40 

05-35 

50-39 

05  '35 

56-06 

1 1  '59 

16  -40 

11  '59 

50  -39 

1 1  '59 

56-06 

30  -04 

26-95 

22  -52 

56  -90 

]7  '00 

56-90 

38  '20 

54-00 

14  '28 

50  -85 

14  -28 

01  -15 

12-86 

50  -85 

1 2  -86 

01  -J5 

49 '3° 

50-85 

49 -30 

01  -15 

18  -04 

39  -oo 

17 '50 

54-90 

26  '02 

15  -30 

59-00 

53-00 

44  74 

06  -60 

Latitude. 


7 
5 

7 
7 
5 
7 
5 
6 

5 
6 

7 
7 
6 
6 

7 
8 
8 
7 
7 
8 
6 
Indiscriminate  mean  =  42°  59'  12''  -91. 


2 

42  59  12-97 

0  -00 

2 

12-88 

+0-09 

2 

12  -69 

+0-28 

2 

13-49 

-0-52 

2 

13  -oS 

—0  -II 

2 

i3-'5 

-0-18 

4 

12-35 

+0-62 

3 

12-86 

+0  -II 

3 

13-69 

—0  -72 

5 

13-03 

—0  -06 

2 

12-68 

+0-29 

2 

12  -22 

-f  0  -75 

2 

13  -04 

—0  -07 

2 

12  62 

+0-35 

2 

12-33 

+0-64 

3 

12  -10 

+0-87 

6 

13-34 

-0-37 

6 

13-44 

-0-47 

6 

II  -89 

+  1  -08 

6 

13  -70 

-0-73 

5 

13-52 

-0-55 

Weighted  mean 


-97  ±  o  '  '09. 


=  42    59    12 

e  =  dn  l'^  '12. 
137  observations,  21  pair.s. 

[Reduction  to  A  =  ^  o"  -10.] 

Unkouoounc,  New  Hampshire. — J.  S.  Ruth.     Zenith  telescope  No.  5.    September  16  to  October 
One  division  of  level  =  i"-o64.     One  turn  of  micrometer  =  46"-6i5  from  circumpolar  observa- 


17- 
8,  1848. 
tions  at  this  station. 

Pairs  of  .stars. 


6  372 

6  468 

6  496 

6  547 

6  583 

6  648 

6  697 

6  777 

6  813 

6  830 

6  865 

6  915 

6  965 

7  022 

7  048 

7   112 

7   153 

7  204 

7  281 

7  36S 

7  480 

7  554 

7  614 

7  727 

Adopted  seconds  of 
mean  N.  P.  D. 

// 

// 

42  -02 

19-13 

07  -00 

23  '59 

53  'OO 

21  -01 

31  -50 

16  -38 

56-42 

29-86 

14-40 

35 '56 

02  -38 

37-95 

37-61 

32-51 

22  -60 

47 '13 

45-25 

38-20 

40-10 

58  -50 

23  -82 

32-06 

»' 

20 

Latitude. 

V 

0        / 

1/ 

// 

3 

5 

42     58 

59  -29 

+0-05 

3 

5 

59-50 

—0  -16 

5 

8 

58  -77 

-fo-57 

6 

9 

59-12 

-I-0-22 

6 

9 

59-07 

+  0-27 

4 

7 

58-77 

+  0-57 

3 

5 

58-20 

+  1  -14 

4 

7 

59  "07 

+0-27 

5 

8 

58-92 

.+0-42 

7 

10 

59 '61 

—0-27 

4 

7 

58 '71 

-fo-63 

4 

7 

58-99 

+0-35 

THE   ASTRONOMIC   MEASUREvS. 


279 


I'airs  of  stars. 


17.    UnkouooHHC,  Maine — continued. 

.\doi)tcd  seconds  of  , 

moan  N.  P.  D.  "  '" 


I 


I 


7  765 

7  «94 
S  054 

8  268 
8  296 

120 

173 
224 

337 
441 

535 
610 

673 

821 

921 

I  066 

J  175 
I  424 


7  S45 

8  023 
8  097 
8  2S4 

«  355 

146 

198 

244 

404 

502 

581 

644 

772 

897 

I  001 

1    123 

I   293 

I  520 


15  'oo         II  'lo  4 

2 1  •  1 1  23  'OO  2 
03  'oo  46  '(x)  3 
40  -30  1 1  '44  4 
25  'S"  50-92  3 
28  '92         1 1  73              4 

35  'OO         54  70  J 

36  -26  06  -34  4 
4>  '15         10-25  3 

44  'lo  42  'OO  3 
02-55  12  71  4 
09  '68  42  80  3 
38  -88  49  -28  3 
oS  "60  23  '48  4 
16 -GO        35-80              3 

22  02        54  -56  3 

45  ■''^3  35-14  4 
00  -00        49  -50  3 

Indiscriminate  mean  =  42°  58'  59"  '37. 

Weighted  mean  =  42  58    59     -34 

('  =  ±0"  -67. 
115  observations,  30  pairs. 

[Reduction  to  A  =  o"  -oo.] 
18.    Thoiiipsoii,  ^Massachusetts.  — T.  J.  Lee.     Zenith  telescope,  Military  Acadenn 
to   October    16,    1S46.     One   division    of   level  =1" -32. 
observations  at  this  station. 


Latitude. 

o      /         // 

42  5«  59  -65 
59  -66 
59  •71 
59-6fj 

59  '^> 
5'^  '4' 

59  '"2 

58  -88 

60  -36 

59  -40 
60-13 
59  47 

59  5 1 

60  '60 

58  -85 
60-68 

59-47 

59  98 

:  o"  -07. 


-0-31 

— o  32 

-0-37 

— o  -26 
— o  -46 

+093 
+0-32 

-ro'46 

—  I  "02 

— 006 

-079 

0-13 

~  017 

-  I  -26 
^049 
-I  "34 
-0-13 
— o  -64 


One   turn    of    micrometer  = 


September  19 
45"  "064,   from 


I 


Pairs 

of  stars. 

-\dopted  seconds  of 
mean  N.  P.  D. 

«' 

w 

Latitude. 

V 

// 

// 

0      / 

" 

ff 

*6  640 

6 

690 

41  -46 

36-72 

II 

6 

42   36 

37  -16 

-0-S6 

*6  640 

6 

691 

41  -46 

17-04 

5 

3 

38-16 

— 014 

6  737 

6 

810 

27-48 

37-30 

9 

S 

38-72 

—0-70 

6  861 

-6 

966 

00-77 

30-14 

3 

2 

38-72 

—0-70 

6  S62 

■*6 

966 

34-07 

.iO- 14 

12 

7 

37  -82 

-ro-2o 

7  024 

-t 
t 

143 

50  -20 

15-50 

14 

II 

37  -38 

+0-64 

7  246 

7 

310 

35-" 

42-50 

14 

II 

38  -89 

-0-87 

7  418 

7 

4S2 

04  -So 

43-00 

13 

II 

37  99 

-fo-03 

7  595 

7 

627 

18  -20 

50  -20 

5 

5 

37  -97 

+005 

7  651 

7 

706 

'5-95 

1 8  ■<xi 

7 

7 

37  -88 

+0-I4 

7  Si  2 

7 

9"4 

35  -43 

40  95 

12 

ID 

38  -48 

—0-46 

7  973 

8 

052 

16-80 

43  -60 

12 

10 

37  -49 

-to -53 

8  104 

8 

182 

28  -20 

iS  -oo 

12 

10 

37-97 

-t-o-05 

1 

n. 

iscriminatc 

niean  = 

42° 

36' 

i&"  -05. 

Weiijhtod  mean          = 

=42 

36 

38 

-02::: 

0"    10. 

('= 

=  ^0 

"•87 

. 

I 

29 

observation 

s,  13  p; 

irs. 

[Reduction  to 

A  = 

=  +o"- 

25.] 

2  So 


THE    EASTERN    OBLIQUE    ARC. 


19.  IVacliiisctt,  Massachusetts. — J.  H.  Toonier.  Zenith 
16,  i860.  One  division  of  level  =o''"9r,  from  observations 
=  4i"'4i3,  from  circumpolar  observations  at  this  station. 


telescope  No.  5.    September  25  to  October 
at  this  station.     One  turn  of  micrometer 


Pairs  0 

f  stars. 

6  654 

6  662 

6  69S 

6  723 

6  764 

6  777 

6  851 

6  865 

6  895 

6  915 

6  932 

6  96S 

7  007 

*7  073 

7  062 

*7  073 

*7  073 

7  091 

7   158 

7   171 

7  215 

7  256 

7  301 

7  320 

7  337 

7  345 

7  368 

7  401 

7  431 

7  453 

7  474 

7  533 

7  57' 

*7  605 

7  5S6 

*7  605 

7  646 

7  721 

7  676 

7  73' 

7  749 

7  798 

7  S12 

7  9'4 

7  932 

*7  983 

7  94S 

7  962 

*7  983 

7  994 

8  054 

*8  079 

8  075 

*8  079 

8  126 

8  136 

8  212 

8  224 

8  277 

8  296 

*8  324 

8  344 

*8  324 

8  366 

*8  324 

46 

Adopted  seconds  of 
mean  N.  1'.  D. 

"' 

2i' 

// 

// 

22  -35 

17  -63 

5 

7 

33  70 

43 '15 

8 

'3 

21  -19 

33  73 

6 

1 1 

1 1  '93 

20  -68 

8 

13 

00  -17 

40  -08 

7 

12 

37  -09 

59-74 

7 

12 

22  -04 

37  '95 

6 

5 

46-54 

37-95 

8 

7 

37  -95 

02  -23 

8 

7 

49-66 

06  -24 

7 

12 

17-17 

22-34 

6 

II 

26-64 

39  '39 

9 

14 

18  -75 

45 '46 

6 

II 

43-80 

20-14 

6 

II 

35-45 

08  -60 

8 

13 

22  -60 

47-04 

7 

12 

49-14 

22  -46 

7 

8 

59  '94 

22  -46 

7 

8 

12  -78 

36  -20 

7 

12 

30  -20 

25  '53 

8 

'3 

17  -07 

24  -30 

7 

12 

21  -96 

I9'i5 

7 

12 

5' -78 

40  -03 

7 

S 

28-08 

12-97 

7 

[2 

40-03 

33  '40 

7 

s 

ro  -36 

28  -34 

9 

9 

33-90 

28-34 

9 

9 

08  -91 

52-90 

8 

13 

06  -ro 

00  -02 

6 

II 

03-60 

26  -00 

7 

12 

II  -74 

24-50 

7 

6 

II  -74 

56-90 

7 

6 

II  -74 

42  -lo 

8 

7 

Latitude. 


42    29 


-68 

■25 
■81 

•87 

6  29 

5 '75 
6-49 
6-36 
6  67 
5-75 
6-34 
6-23 
5 '94 
5-68 
5 -So 
5-'4 

5  -95 
5-96 
6-65 
6-77 
6-49 

6  -29 

6-65 
6-66 
6-58 
5-85 
5-45 
5-95 
6-15 
5-78 
5-67 
5 -7' 
5-27 


+  0  -45 
— o  -12 
+0  -32 
+0  -26 
— o  -t6 
+0-38 
—0-36 
— o  -23 
—0-54 
+0  -38 

— O  -21 

— o  -lo 

+  0-19 
+  0-45 
40-33 
+0-99 
+  0-18 

+0-I7 
—0-52 
—0-64 
-0-36 
-  -0  -16 
-0-52 
- -o  -53 

-0-45 
+0-28 

+0  -68 

-fo-i8 

— O  "02 

+  0  -35 
+  0-46 
+0-42 
+  0-86 


THE   ASTRONOMIC   MEASURES. 


281 


19.    li'adnisf/l,  Massachusetts — continued. 


* 


I 


Pairs  ( 

jf  stars. 

92 

109 

130 

175 

229 

244 

285 

3'4 

339 

345 

412 

446 

469 

498 

535 

556 

576 

*59o 

579 

•"•590 

656 

673 

706 

761 

802 

83S 

dopted  seconds  of 
mean  N.  P.  D. 

// 

// 

03  '44 

13  -69 

37  ■4" 

15-60 

oS  -yS 

10 -68 

52  •4'^ 

"5  7 ' 

45  7" 

'5-99 

08  -90 

09  -44 

20  -78 

01  -35 

24  -84 

18  -68 

40-27 

55  '9" 

38  -08 

55  '90 

36  -So 

13  -10 

05  -80 

22  -40 

24-50 

51  '9" 

Latitude. 


7 

12 

6 

II 

6 

1 1 

7 

12 

7 

12 

6 

II 

6 

II 

6 

II 

7 

S 

7 

S 

8 

13 

6 

1 1 

6 

II 

42 


16-78 

-0  -65 

16-65 

0-52 

'5  77 

i  0  -36 

16-03 

-^o-io 

16  01 

-  012 

16  -60 

-0-47 

17-07 

0-94 

16-57 

-  0  -44 

15-95 

+0-18 

16-16 

0-03 

16  09 

-  0  -04 

15-84 

-{  0  -29 

16  12 

-i-o-oi 

Indiscriiuinate  iiieaii=42°  29'  i6"i2. 
■Weighted  mean  =42    29    16    -i3±o"-o4. 

^=±:o""6o. 
322  ob.servations,  46  pairs. 

[Reduction  to  A=  -^o"-95-] 

20.  Harvard  College  Observatory,  Cambridge,  Ma.ssachusetts. — The  report  of  Dr.  R.  A.  Gould 
to  tlie  Superintendent  of  the  United  States  Coa.st  Survey,  dated  Cambridge,  November,  1865,  and  printed 
in  the  Report  for  1865,  gives  the  following  information  respecting  the  latitude  of  this  observatory: 

"  Prof.  B.  Peirce  in  1845  found  from  transit  observations  in  the  prime  vertical  by  Messrs.  W.  C. 
Bond,  J.  D.  Graham,  and  G.  P.  Bond  the  following  values  for  the  latitude  of  the  observatory: 

W.  C.  Bond,  62  observations,     42^  22'  48"  -83 
J.  D.  Graham,  41  observations,  48     -29 

G.  P.  Bond,  65  observations.  48      86 


Mean  bv  weights 


42    .72    48     -60 


"This  restilt  has  been  used  to  the  present  time.  The  adoption  of  later  determinations  of  the 
declinations  of  the  5  stars  observed  would  .somewhat  diminish  the  restiltant  value;  but  there  seems 
little  doubt  that  this  value  should  be  lessened  by  about  half  a  second,  unless  strong  local  disturl)ances 
of  the  plumb-line  exist  in  the  vicinity."'"' 

Other  references  will  be  found  in  the  American  Ephemeris  and  Nautical  Almanac  for  1855  and 
in  Memoirs  of  the  American  Academy  of  Natural  Sciences,  II,  203. 

The  reduction  to  the  center  of  the  dome  is  0^-55,  hence  the  latitude  of  the  dome  42^  22'  48"-o5 
with  estimated  proliable  error  zbo''''-22  which  is  adopted. f 


*This  last  remark  has  no  bearing  on  the  result  here  needed. 
tThe  Ephemeris  for  iSSS  givts  .(2°  22'  48"-,v.  and  that  of  1SS9,  42 


2'  47"6,  for  which  v.iUus  no  explanation  is  offered. 


282 


THE    EASTERN    OBLIQUE    ARC. 


2 r .    Cloverdi -11   Ohsen 
Peters.     Zenith  telescope 


•atory ,  Cambridge,  Massachusetts.* — B.   .\.  Gould,  J.  Searles,  and  C.  H.  F. 
No.  5.     August  to  October,  1S55.     One  division  of  level  =o""SS.     One  turn 


of  micrometer 

=4i''-369. 

Pairs  of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

n' 

w 

I.atitude. 

1/ 

// 

// 

0          /             // 

// 

6 

372 

6  426 

20  70 

15-11 

18 

9 

42    22   40-79 

+0-18 

6 

452 

6  497 

3878 

17-17 

20 

9 

40-36 

+0-61 

6 

7  28 

6  769 

59  '05 

21  -26 

18 

9 

41  -83 

-0  -86 

6 

86 1 

6  S82 

36  -40 

55;43 

17 

8 

41  -40 

-0  -43 

6 

912 

6  932 

02  71 

28  -75 

21 

9 

39-86 

+  r-ii 

7 

073 

7  091 

36-14 

01  -98 

21 

9 

41  -31 

-  0  '34 

7 

15S 

7   171 

51  -81 

09  -23 

19 

9 

40  -65 

+0-32 

7 

1 88 

7   193 

42  -34 

'3 '63 

19 

9 

41  '53 

--  0  -56 

7 

219 

7  297 

03 '34 

51  -01 

18 

9 

40  -81 

+0-16 

7 

368 

7  401 

56-26 

35  '34 

17 

8 

40-69 

+0-28 

7 

431 

7  453 

51  -20 

25  -16 

16 

8 

40  -88 

+0-09 

7 

,503 

7  521 

51  -13 

08  -56 

15 

8 

4t  -30 

-0-33 

7 

765 

7  800 

10  '30 

32-35 

12 

8 

41  -13 

—0  -16 

7 

950 

7  978 

46-46 

06 -So 

12 

8 

41-78 

~o  -81 

S 

054 

8  079 

47  '34 

04-57 

14 

8 

41  -31 

-0-34 

8 

284 

8  310 

50 '33 

26  -02 

12 

8 

41  -21 

—0  -24 

8 

324 

8  344 

51  '07 

04-50 

12 

8 

40-41 

-+0-56 

92 

109 

43  70 

53  -78 

10 

7 

40-37 

+0  -60 

' 

158 

219 

55  '22 

25  -28 

n 

8 

40-84 

+0-13 

[Reduction  to 

Indiscriminate  mean  =42°  22' 
Weighted  mean           =42     22 

e  =±o"-67 
302  observations,  19  pairs, 
center  of  dome  of  Harvard  Col 

40' 
40 

ege 

■97- 
-97±o''-o8. 

Ob.servatory  =-j-7''' 

20.] 

22.  JMoiint  Tom,  Massachusetts. — E.  Goodfellow.  Zenith  telescope  No.  5.  July  iS  to  August  11, 
1862.  One  divi.sion  of  level  =o"-76  from  observations  at  this  .station.  One  turn  of  micrometer 
=  4i''-38o  from  circunipolar  observations  at  this  station. 

h'  w  Latitnde.  v 


Pairs  c 

)f  stars. 

5   157 

5   '68 

5  249 

5  252 

5  295 

5  338 

5  376 

5  453 

5  463 

5  496 

5  5 12 

5  5.30 

5  549 

5  619 

5  602 

5  643 

5  624 

5  629 

5  775 

5  790 

adopted 
mean 

seconds  of 
N.  P.  D. 

// 

// 

25  -88 

43  -oo 

23-24 

'  7  -.25 

08  -47 

42-79 

30-19 

49  -83 

23  -oo 

22  -67 

21  -76 

16-74 

57  -65 

19-40 

52  -26 

14-21 

15  -64 

18-76 

54-97 

05-14 

3 

42  14  27  -08 

+0-54 

7 

27  -61 

+0-0I 

7 

28  -20 

-0-58 

6 

28  -oo 

-0-38 

8 

27-48 

+0-14 

8 

28  -33 

-071 

7 

27-52 

+  0  -JO 

7 

27  -60 

+  0-02 

7 

28  -32 

^0  -70 

7 

26-49 

+  I-I3 

*See  report  by  Dr.  B.  A.  Gould  dated  November,  1865,  in  U.  ,S.  Coast  .Survey  Report  for   1S65.     These  results  were 
revised  and  in  part  improved  in  1S70. 


THE   ASTRONOMIC   MEASURES. 


283 


22.  Mount  Tom,  Massachusetts — contiiiue'l. 


Pairs  of 

stars. 

Adopted 
mean 

seconds  of 
N.  P.  D. 

n' 

•M 

Latitude. 

V 

f  / 

// 

G      /         //  . 

// 

5  763 

5  776 

20.  25 

16  -56 

6 

8 

42    14   27  -89 

—0  -27 

5  795 

5   «42 

51  '53 

56  -08 

5 

7 

27-57 

•  fj  -05 

5  944 

5  997 

25  -05 

34  -80 

5 

7 

28-12 

—0-50 

6  013 

6  062 

13  'lO 

08  -91 

4 

7 

27  -06 

+0-56 

6  021 

6  079 

46  '00 

16-63 

4 

7 

28-70 

-I  -oS 

6  109 

6  193 

2577 

46  -gS 

4 

7 

26  -83 

-0.79 

6   147 

6  185 

19-41 

15-68 

4 

7 

27-56 

-  0-06 

6  162 

6  218 

12-05 

58  -43 

5 

7 

28-05 

-0-43 

6  300 

6  373 

22  -39 

00-18 

5 

7 

27  -60 

+0  02 

6  341 

6  410 

13  -82 

5>  -41 

3 

6 

27-09 

^0-53 

6  466 

6  516 

28-62 

35-12 

5 

7 

27  95 

-0-33 

6  475 

6  493 

03 '"S 

3'  -03 

4 

7 

26-66 

0  -96 

6  534 

6  551 

35  '24 

51  -12 

5 

7 

27  00 

T  0  -62 

6  530 

6  553 

16-57 

47-72 

5 

7 

27-96 

-0-34 

6  655 

6  602 

45  29 

12-25 

5 

7 

26-78 

-fO-84 

6  659 

6  698 

50-65 

17  -80 

5 

7 

27-23 

-0-39 

6  718 

6  745 

17-11 

55  -49 

5 

7 

28-14 

-0-52 

6  740 

6  748 

45-32 

56-32 

5 

7 

27 -oS 

-0-54 

6  771 

6  799 

38-24 

56-31 

5 

7 

27  -86 

-0-24 

6  827 

6  834 

41  -92 

42-35 

5 

7 

27-75 

-0-13 

6  847 

6  S79 

14  -06 

31  -87 

6 

8 

28 -iS 

-0-56 

6  862 

6  882 

03  -06 

48  -48 

5 

7 

27-67 

-0-05 

6  930 

6  941 

24-48 

25-44 

5 

7 

27  23 

-  0    39 

6  957 

6  976 

16-56 

12-58 

5 

7 

27-36 

+0-26 

6  985 

6  998 

28-51 

46-80 

6 

8 

27-15 

+  0-47 

7  073 

7  091 

15-92 

37 -So 

5 

7 

28-72 

—  I  -10 

Indiscriminate  mean 

=42°  14'  27' 

'-61. 

Weighted  mean 

=42    14   27 

-62zizO'^-o6. 

C 

=  ±o"-45. 

172  observations,  36  p 

airs. 

[Reduction  to  A  =+o"-9i.] 


284 


THE  eastb:rn  oblique  arc. 


23.  Manomet,  Massachusetts.  — C.  O.  Boutelle,  F.  H.  Agnew,  and  C.  S.  Peirce.  Zenith  telescope 
No.  5.  July  S  to  August  2[,  1867.  One  division  of  level  =  o"  '951  from  observations  at  this  station. 
One  turn  of  micrometer  =  \\"  '423  from  circumpolar  observations  at  this  station. 


Pairs  of  stars. 

4  812 

4  S43 

4  S73 

4  949 

4  961 

4  974 

5  05  s 

5  085 

5  '«' 

5  204 

5  336 

5  463 

5  512 

5  525 

*5  54 1 

5  574 

*5  541 

5  575 

5  62.S 

5  702 

5  714 

5  797 

5  847 

*5  «7i 

*5  871 

5  •'^SS 

*5  931 

5  950 

*5  931 

5  951 

*5  997 

6  062 

*5  997 

6  06S 

*6  1S5 

6  232 

*6  185 

6  237 

6  341 

6  373 

6  429 

6  470 

6  522 

6  547 

6  57' 

6  623 

6  637 

6  681 

6  698 

6  734 

6  763 

•■<-6  784 

6  764 

-6  784 

6  8ro 

6  932 

6  962 

*6  990 

6  965 

*6  990 

7  062 

7   103 

5  168 

5  271 

5  295 

5  388 

5  444 

5  459 

5  530 

5  560 

5  602 

5  752 

5  795 

5  863 

5  927 

5  937 

*6  223 

6  311 

*6  223 

6318 

tl  631 

*6  427 

Adopted  seconds  of 
mean  N.  P,  D. 

// 

// 

31  '30 

13  -40 

15  -GO 

14-00 

18-20 

36-60 

52  "26 

08  -20 

30  -50 

45  -00 

59  'oo 

06  -90 

03-00 

06  -OO 

12  -40 

53-60 

12  -40 

26-80 

31  '40 

06  -00 

23  "37 

25-30 

02  -80 

39-00 

39  'oo 

47-10 

37  '47 

26-50 

37  -47 

08  -70 

45  '05 

13-54 

45  '05 

54  -80 

07  '85 

22  -73 

07  '85 

05  -41 

00-60 

44-10 

23  "95 

21  -[2 

54  "08 

42-92 

r  I  -30 

33  -50 

25  -50 

25  -60 

40  -QO 

09-67 

56  -38 

48-50 

23-90 

48-50 

31  -GO 

24-74 

07  'OO 

43-02 

38-12 

43-02 

24-40 

II  -48 

42  -So 

30-00 

01  -00 

54  -40 

57  'OT 

18  -40 

56-94 

50-99 

29  "54 

55  -80 

.6-72 

31-01 

24-95 

56  -80 

25-50 

37-50 

25  -50 

20  -80 

17-75 

03  -82 

Latitude 

V 

/        // 

// 

55  34-56 

+079 

35-12 

+0-23 

34  -94 

+0-41 

35-31 

+0-04 

35-61 

—0  -26 

35  -23 

-|  0  -12 

35  -56 

—  0  -21 

34-24 

+  I-II 

34  -04 

+  1-31 

35  -92 

-0-57 

34-47 

+0-88 

35-11 

+0-24 

35-74 

-0  -39 

35  -82 

-0-47 

35  -84 

-0-49 

35-80 

•-0-45 

35  -48 

-0-13 

34-83 

+0-52 

36-53 

-1  -18 

33-99 

+  1-36 

35  -75 

—0  -40 

34-36 

+0-99 

34-82 

+0-53 

35  -29 

+0-06 

34 -Si 

+0  -54 

35-46 

— Q-II 

35-43 

-0-08 

35-55 

—0-20 

36-24 

-0-89 

36-00 

—  0-65 

35-06 

fO-29 

34  90 

+0-45 

35  -66 

-0-31 

36-81 

-r-46 

36-72 

- 1  37 

34  -80 

+0-55 

3670 

-I  '35 

35  -87 

-0-52 

35  -08 

+0-27 

34-72 

+0-63 

36-70 

-I. '35 

THE    ASTRONOMIC   MEASURES. 


285 


23.  A/anoinci,  Massachusetts — continued. 


Pairs 

of  stars. 

Adopted  stc 
mean  N. 

OIKlS  Ot 

I'.  D. 

n' 

w 

Latitude. 

V 

// 

// 

0      /           // 

ff 

tl    633 

*6  427 

21  -25 

02,  -82 

6 

3 

41  55     34  -85 

+0-50 

6  456 

6*520 

34-62 

08  -00 

5 

5 

35  -82 

-0-47 

6  530 

6  534 

50  -92 

09-19 

5 

5 

35-91 

-0-56 

6  5.S2 

6  629 

53-36 

04-14 

5 

5 

34-02 

-i-I  -33 

6  673 

X  2    872 

09  '04 

25-16 

6 

5 

34-63 

+0-72 

6  714 

6  748 

39  '9" 

13-50 

6 

5 

34-73 

+0-62 

6  75« 

6  867 

4071 

30  '44 

5 

5 

34-42 

-fo-93 

6  973 

6  976 

31-50 

18 -20 

5 

5 

35-24 

-fo-ii 

7  035 

7  067 

IS -53 

25-20 

6 

5 

34-43 

+0-92 

7  055 

7   '52 

02  -17 

45-62 

6 

5 

35  62 

-0-27 

7  215 

7  246 

47-65 

57-30 

5 

5 

35-71 

-036 

7  256 

7    28 1 

47-80 

25-30 

6 

5 

35-43 

-0-08 

7  306 

7  320 

56-35 

01  -20 

6 

5 

35  -30 

-fo-05 

5  321 

5  341 

30-50 

48  -69 

2 

4 

35  -60 

-0-25 

5  535 

5  619 

52-27 

56-15 

3 

5 

34-45 

+0-90 

5  747 

5  853 

14-64 

54-19 

8 

5 

35-39 

—0  -04 

5  978 

6  106 

24-18 

04-14 

6 

5 

35-55 

— 020 

6  23S 

6  36cS 

27-78 

37-64 

7 

5 

35-33 

-f  0-02 

6  497 

6  530 

19  -57 

50  92 

6 

5 

35-68 

-0-33 

6  603 

6  698 

46  -00 

40  'OO 

6 

5 

35-43 

-0-08 

6  745 

6  769 

15  -20 

40  -88 

7 

5 

35-78 

-0-43 

6  S47 

6  940 

27  90 

16  -70 

7 

5 

35  47 

—0-12 

6  983 

6  997 

35-50 

53-00 

7 

5 

36-15 

— oSo 

7  041 

7   119 

44-76 

07  -44 

6 

5 

36  16 

— oSi 

7  143 

7   176 

55-00 

30  50 

7 

5 

35-59 

-024 

7  204 

7  243 

35-44 

38  -09 

5 

5 

34  90 

-0-45 

7  253 

7  260 

54  -48 

06-98 

5 

5 

35-64 

— 029 

7  277 

7  333 

36-50 

05  30 

6 

35-66 

-0  -31 

7  385 

7  455 

16  -22 

38  ■  1 2 

6 

35-68 

-033 

?5  241 

7  5<'5 

01  -30 

39  -30 

35-32 

-roo3 

7  533 

II  4  739 

52-74 

30  94 

33-98 

+  1  -37 

7  542 

7  585 

02-52 

44-70 

36  -52 

-1    17 

7  623 

7  636 

39  -55 

49  67 

35-29 

+006 

7  696 

■^-  7  706 

45-94 

12  -22 

34-86 

+0-49 

7  698 

*7  706 

38  -55 

12  -22 

35  -32 

+0-03 

7  754 

7  757 

]6  '20 

57  -06 

5 

35  65 

—0-30 

Indiscriminate  mean      ^41°  55'  35"-36. 
■W^eighted  mean  =41     55    35    -35  d 

C  =  2rO"-30. 

456  observations,  77  pairs. 

[Reduction  to  A  =  o"-oo.] 


o"-05. 


tGreenwich,  12-year  catalogue. 


I  Groombridge. 


\  Radcliffe 


I  .-Vrmagh. 


286 


THE   EASTERN   OBLIQUE   ARC. 


24.  Sand/ord,  New  York. — E.  Goodfellow.     Zenith  telescope  No.  5.     September  11  to  Octobers, 
1862.     One  division  of  level  =  o"-6'6-].     One  turn  of  micrometer  =  4i"'4o. 


Pairs  c 

)f  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

n' 

W 

Latitude. 

V 

// 

/ ' 

c 

>       /          // 

f/ 

6  421 

6 

468 

10 '54 

18 -iS 

2 

4        4 

I    27   41  -ID 

-0-63 

6  427 

6 

470 

21  -44 

43-64 

4 

5 

40-55 

-o-o8 

6   475 

6 

495 

03  'I5 

17  -94 

5 

5 

39-46 

+  1  -QI 

6  520 

6 

556 

32  "56 

49-71 

3 

5 

40  -35 

-f  0  -12 

6  530 

6 

571 

16-54 

40-61 

3 

5 

41  -46 

-0  -99 

f  555 

6 

5  89 

45-29 

03  -05 

3 

5 

40-50 

—0-03 

6  629 

6 

652 

36  -40 

5'  -67 

5 

5 

39-24 

+  1  -23 

6  698 

6 

717 

17  -87 

12-73 

5 

5 

40  -80 

-0-33 

6  731 

6 

765 

30  '32 

20-21 

5 

5 

41  -GO 

-0-53 

6  779 

6 

806 

16  '02 

08  -63 

5 

5 

39-74 

+  0-73 

6  818 

6 

827 

39  77 

41  -23 

5 

5 

39 -84 

+0-63 

6  861 

6 

866 

2970 

20  -41 

5 

5 

40-28 

+0-19 

6  867 

6 

882 

18-43 

48-14 

5 

5 

40-50 

-0-03 

6  937 

6 

962 

52-17 

00-85 

5 

5 

41  -08 

— o-6i 

6  965 

6 

967 

31  '46 

51  -70 

5 

5 

40-78 

-0-31 

6  970 

6 

975 

19 '59 

18  -96 

5 

5 

40-78 

-0-31 

7  027 

7 

041 

48  -64 

42-55 

5 

5 

40  -11 

+0-36 

7  013 

7 

060 

30  '34 

01  -41 

5 

5 

40  -61 

— 0-14 

7  0S4 

7 

112 

38-26 

42-64 

5 

5 

40-21 

+0-26 

7   120 

7 

164 

14  -32 

53  -66 

5 

5 

41-52 

-I  -05 

7   153 

7 

194 

28-30 

56  -08 

5 

5 

40-52 

—0-05 

7  182 

7 

204 

15-88 

41  -47 

3 

5 

39-08 

+  1  -39 

7   19S 

7 

213 

10-26 

51  -72 

3 

5 

40-30 

+0-17 

7  220 

/ 

275 

46  -93 

19  -00 

5 

5 

40-99 

-0-52 

7  297 

7 

333 

II  -23 

16  -lo 

5 

5 

40-47 

0  -00 

7  345 

7 

373 

17-46 

04  -ID 

5 

5 

41  -09 

—0-62 

7  365 

7 

368 

57-34 

14  -60 

5 

5 

39-u 

+  1-36 

7  3«7 

7 

410 

15-27 

24-12 

5 

5 

39-87 

+0  -60 

7  418 

7 

449 

02  -07 

53  -50 

5 

5 

41  -42 

-0-95 

7  455 

7 

462 

55  '34 

53  -56 

5 

5 

39-58 

-1-0-89 

7  474 

7 

495 

50-94 

54-45 

5 

5 

40-38 

+0  -09 

7  503 

7 

505 

00  -96 

58-97 

5 

5 

40-79 

—0-32 

7  544 

7 

554 

04  "43 

II  -92 

5 

5 

40-38 

+0-09 

7  571 

7 

5S2 

13-99 

06  -68 

5 

5 

41  -30 

-0  -83 

7  585 

7 

595 

07  -30 

54-97 

5 

5 

41  -39 

—0  -92 

Inc 
We 

161 

liscriminate  mean      =41^ 
ighted  mean               =  41 

observation.s,  35  pains. 

[Reduction  to  A  = 

27'  40'' 
27  40 
''-39. 

-  o"-39 

•47- 
-47  ±0 

•] 

''  -08. 

THE    ASTRONOMIC    MEASURES. 


287 


25.  M'^es/  Hills,  New 
division  of  level  =  o"i6 
circiuiipolar  observations 


York.— A.  T.  Mosinan.  Zenith  telescope  Xo.  5.  Auj(ust  8  to  24,  1865.  One 
from  observations  at  this  station.  One  turn  of  micrometer  =  4 1 "397  from 
at  this  station. 


I 


Pairs  of 

star.s. 

Ado])ted  secoiid.s  of 
mean  N.  P.  D. 

n' 

w 

Latitude. 

V 

// 

// 

0      /        // 

// 

5  617 

5  644 

08  '60 

07-17 

6 

16 

40  48  50  -85 

-0-79 

5  643 

5  677 

34-15 

52  -20 

4 

14 

49-69 

+0-37 

5  65<S 

5  703 

CKJ  "26 

57  ■«2 

2 

10 

50  -3  1 

-0-25 

5  7"2 

5  734 

54  ■>J9 

20-97 

4 

14 

49  67 

+0-39 

5  714 

5  801 

1 2  '37 

33  -63 

6 

16 

49  5' 

-f-o-55 

5  752 

5  798 

44-57 

42-17 

4 

14 

49-66 

+0-40 

5  «4o 

5  856 

17  'OO 

03  -62 

6 

16 

49  -69 

+0-37 

5  842 

5  9'i 

08 -18 

30-90 

6 

16 

50-14 

—0  -08 

5  874 

5  944 

26  -89 

33  •■•S 

7 

16 

49-97 

+0-09 

5  922 

5  95'> 

06-55 

21  -74 

6 

16 

49  69 

+0-37 

5  97S 

6  030 

16  -50 

57-54 

4 

14 

49-99 

+0-07 

6  005 

6  079 

39-91 

18-50 

5 

15 

50-27 

—0-21 

6  013 

6  082 

18  -60 

46-33 

4 

14 

50-14 

—0-08 

6  147 

6  246 

19  -20 

36-34 

6 

16 

50 -86 

— 080 

6  231 

*6  311 

34-70 

43-54 

6 

10 

50-33 

-0-27 

6  251 

*6  3 1 1 

'9-5« 

43-54 

7 

II 

49-91 

+0-15 

6  373 

6  43« 

50  -58 

06*00 

6 

16 

49-76 

+0-30 

6  3«7 

6  410 

49  -80 

40-32 

6 

16 

49  -53 

+0-53 

6  421 

6  427 

59-06 

09  -70 

6 

16 

50-17 

— o-ii 

6  468 

6  516 

04-95 

20-19 

0 

16 

50-06 

0-00 

6  473 

6  493 

06-94 

16  -96 

6 

16 

49  -75 

+0-31 

6  534 

6  566 

1974 

08  -09 

5 

15 

50-22 

— 016 

6  553 

6  579 

32-65 

49  -90 

6 

16 

49-52 

-ro-54 

6  581 

6  656 

04  -86 

24-97 

6 

16 

50-21 

-0-15 

6635 

6  690 

26-65 

17  -90 

6 

16 

50  -40 

-0  -34 

6  698 

6  721 

57  -50 

42  -01 

6 

16 

50-07 

— 001 

6  711 

-6  728 

49-64 

40  -82 

7 

II 

49-94 

+0-12 

*6  7  28 

6  765 

40  -82 

53-"S 

6 

10 

50  50 

-0-44 

6  74S 

6  762 

30  -36 

07-17 

5 

15 

49^83 

+0-23 

6  Sio 

*6  81 8 

50  -75 

12-44 

6 

10 

49-99 

+007 

*6  818 

6  866 

12-44 

51  -90 

6 

10 

49-33 

+0-73 

6  827 

6  863 

14-45 

19-10 

6 

16 

50-93 

-0  -87 

6  868 

6  905 

00  -27 

24  -45 

6 

16 

50  -37 

—0-31 

6  S76 

6  937 

40-77 

23  -10 

6 

16 

50-15 

— 0  -09 

6  915 

6  965 

52  -4S 

00-62 

7 

16 

50  -^^ 

—0  03 

6  966 

6  976 

04-42 

40-94 

6 

16 

49  -87 

+0-19 

6983 

6  998 

56-65 

15-02 

6 

16 

50-15 

— 009 

7  022 

7  041 

25-46 

07  -86 

7 

16 

50  -47 

-0-41 

7  064 

7  117 

19-71 

01  -71 

7 

16 

50  -21 

-0-15 

Im 

iscriminate 

nean      = 

40°  48'  50" 

-06. 

Wl 

iijhted  mean 

,: 

40    48   50 
=to"  -34. 

■06  rb 

0"  -04. 

223  observations,  39  pairs. 

[RodiK-tion  to  Js,=  —  o"-i6.] 


288 


THE    EASTERN    OBUOUE    ARC. 


26.   Ne'iS.'  York,  New  York. — E.  Goodfellow.     Zenith  telescope  No.  5.     June  22  to  25,    1S5S.     (_)ne 


division  of  level  =  o"'845. 

Pairs  of  stars. 


One  turn  of  micrometer  =  i\\"'^i6. 


.\ilopted  .seconds  of 
mean  N.  P.  D. 


I.atitude. 


4  640 
■4  S04 
4  845 

4  885 
*4  952 
*4  952 

5  113 
5  244 
5  336 
5  385 

5  448 
.'S  599 

*5  752 
*5  752 
*5  902 
*5  902 

6  005 
*6  079 

6  251 
6  387 
6  476 
6  534 
6  64S 
6  697 


4  726 
4  SoS 
4  S64 

4  897 

5  000 
5  036 
5  204 
5  313 

*5  400 
*5  400 
5  502 
5  677 
5  798 
5  860 
5  9*57 

5  988 
-6  079 

6  223 
6  31S 
6  410 
6  491 

6  579 
6  687 
6  740 


05  '82  41  '06  3 

05  -42  1 1  -96  3 
41  -90  57  76  4 
13  -08  06  -54  4 
35  -82  49  77  4 
35  "82  1 1  -25  4 
50-58  01  -05  4 
39  •10  51  •66  4 
27  -68  58  -95  4 

45  '50  58  -95  4 

14-58  14-87  4 

20-95  08-13  4 

06  -46  ( )9  -57  4 
06  -46  23-12  4 
29  -36  09  -8 1  4 
29-36  48-41  4 
27  -06  13  "So  4 
13 '80  36-38  2 
29-16  41  -44  3 
II  -34  06  -13  3 
59  '38  09  -58  4 
55  '92  25  -75  4 
13-28  .12-72  4 
16  -61  17  '46  4 

Indiscriminate  mean  =  40°  43'  4.S' 
Weighted  mean  =  40    43    48 

'■=  -to" -45. 
90  observations,  24  pairs. 


4 
4 
5 
5 

3 
5 
5 
3 
3 
5 
5 
3 
,3 
3 
3 
3 
3 
4 
4 
5 
5 
5 
5 

■43- 
■39  =* 


40  43  47  72 
47-72 

47  '28 

48  -06 
48-86 
47-36 
49-10 

47-53 
4S-86 

49  -63 
48  -24 
48  -14 
48  -50 

47  -5« 
4''-i  -95 
48-62 

48  -95 

48  -82 

49  -58 
49-17 
49-13 
48  -06 

48-51 
48  -02 

/'•09. 


^o  -67 
r'5  '67 
t- 1  - 1  [ 

+0-33 
-o  -47 

-^i  -03 
—  o  -71 

ho -86 
-o  -47 

-1  -24 
+0-15 
-fo-25 
— o  -II 
^o-Si 

-o  -56 

-0-23 

-  o  -56 

-'•  -43 
-1  -19 

— o  -78 
-o  -74 

-T-O  -33 
— O  "12 

+0-37 


[Reduction  to  center  of  transit  <>r  A  =  +o''-2i.] 


riUi    ASTRONOMIC    MKAvSURKS. 


289 


27.    I'icacon  Hill    New  Jcrscj  . — J.  P..  liaylor.      Zciiitli  Ic-k-scope  No.  4.     July  24  to  Auj^usl  27,  1875. 
One  division  of  level  =2"u4.     One  turn  of  niiironieler  =43"'462  from  circunipolar  observations  at 


l.his  station. 

I'airs  of  .star.s. 


* 


5  400 

5  432 

\S  463 

5  523 

5  629 

5  703 

*5  Soi 

*5  Soi 

5  931 

5  997 
*6  082 

6  193 
*6  232 
*6  232 

6  300 
6  357 
6  43S 
6  476 
6  530 
6  571 
6  602 
6  697 
6  7  28 
6  Soo 
6  S62 
5  596 

5  951 

6  084 
6  1 84 
6  23S 
6  71 1 

6  745 
6  810 


5  411 

*5  463 

5  479 

5  546 

5  677 

5  7S5 

5  828 

5  860 

5  937 
*6  0S2 

6  095 
6  203 
6  246 
6  258 
6  34S 
6  404 
6  463 
6  497 
6  547 
6  579 
6  68 1 
6  714 
6  771 
6  S30 
6  933 

5  604 

6  "33 
6  09  r 
6  223 

6  335 
6  718 

6  765 
6  867 


Adopted  seconds  of 
mean  N.  \'.  D. 


3 
5 
7 
5 
5 
6 

7 
6 

7 
6 

7 
7 
7 
7 
7 
6 
6 

7 
6 

7 
7 
6 

7 
6 
6 
3 
5 
5 
5 
5 
6 

5 
5 

=40°  22'  27"-84. 

=40    22    27    •Sid=o"-o7. 

(■=rbo"'42. 

195  observations,  33  pairs. 

[Reduction  to  iA=o"'oo.] 


46  •s.s 

0  ^   -(  K  ) 

23  74 

17  '20 

17  -20 

20  -84 

29  -40 

"4-37 

47-64 

56  -oo 

58  75 

53  -32 

22-52 

43  -46 

22-52 

29  -70 

01  -51 

19  -66 

01  -30 

53  -10 

53  ■!» 

16 -61 

37 '14 

56  -45 

1 2  -63 

21  -59 

12  -63 

31  -66 

55-06 

58  -33 

29  -60 

29  -83 

25  '60 

50  -95 

45-92 

41  -16 

10-05 

01  -35 

25  -20 

41  -80 

52  -77 

28  -68 

09  -04 

40-44 

22-43 

47  -42 

28  -50 

24-52 

(X)  -07 

17-42 

35  -60 

10  -20 

29  -So 

ol  -85 

15-09 

44-68 

40  -87 

16-26 

16 -So 

40-07 

32  -99 

36  -89 

09-51 

30  -62 

22  -04 

14-83 

7V 

latitude. 

V 

0      /        // 

// 

6 

40    22    27  -73 

-0  -08 

4 

28-95 

I  -14 

5 

27-77 

:  0  -04 

7 

26-86 

•-0  -95 

7 

26-78 

1  -03 

7 

27-58 

ro-23 

5 

27-59 

4-0-22 

5 

28  -6<) 

-0-79 

7 

28  -15 

'>  -54 

5 

28  -02 

-  f)  -21 

5 

28  -64 

-0-S3 

7 

26-95 

-0  -86 

5 

28  -08 

—0  -27 

5 

27-65 

~o-j6 

7 

28  -30 

-0  -49 

7 

27  -3(j 

-0-51 

7 

28-31 

0-50 

7 

27  -62 

0-19 

7 

27-66 

•  o-iS 

7 

27-41 

-0  -40 

7 

27  -38 

-  0  -43 

7 

27-10 

-0-71 

7 

27-50 

•0-31 

7 

27  -61 

+0-20 

7 

27-46 

-0-35 

6 

27  -39 

-;-o  -42 

i 

28  -24 

-0-43 

7 

28  -I  I 

—0  -30 

7 

27  -87 

— 0  -06 

7 

28-26 

-045 

7 

28  -26 

-045 

7 

28  -67 

-0-S6 

7 

28  -97 

-I  -16 

Indiscriminate  mean 
Weighted  mean 


4192 — No. 


■19 


290 


THE    EASTERN    OBLIQUE   ARC. 


2S.  Mount  Rose,  New  Jersey. — J.  E.  Hilganl.  Zenith  telescope  Nt).  2.  July  19  to  August  3,  1S52 
One  division  of  level  =i''''"oo,  from  observations  at  this  station,  (^ne  turn  of  nncronieter=44"75o, 
from  circunipolar  observations  at  this  station. 


Pairs  of 

stars. 

t2    2S5 

5  302 

5  33S 

5  432 

T     211 

5  383 

1     276 

5  38-' 

5  463 

5  479 

5  4S9 

1  448 

5  62S 

5  686 

5  674 

5  74f 

5  702 

5  728 

5  7S5 

5  922 

5    '^2' 

5  S23 

5  941 

5  972 

5  967 

ii  539 

6   178 

6  255 

6  216 

6  223 

6  322 

%  348 

6  341 

*6  348 

6  460 

6  563 

6  487 

6  586 

6  5«5 

6  625 

6  623 

6  690 

6  648 

6  697 

6  735 

6  749 

*6  817 

*6  817 

adopted 
mean 

seconds  of 
N.  P.  D. 

// 

>' 

52  -45 

25-61 

00-55 

48-80 

13  -So 

40  -84 

3'  '3' 

17  -60 

54  75 

58  -92 

57  '60 

GO  -94 

47-42 

40-14 

24-66 

19  '65 

35-40 

50-42 

59  "46 

26  -36 

14  -rxi 

10  -50 

41  -66 

16-26 

54-96 

43  'lo 

42  •6r 

04  •  1 2 

39  73 

43  "30 

24  -26 

58 -45 

39 '2  1 

58  -45 

05  '74 

49-76 

44-76 

08  -27 

19  -So 

20  -26 

10  -44 

52  -60 

53  77 

01  -73 

26-44 

06  -40 

27-66 

27-66 

IV 

IvStitjuie. 

T 

0      /          / ' 

// 

4 

40    22    05  -GO 

+  0-41 

6 

05  -54 

—  0-07 

4 

05  -26 

+  0-15 

4 

04  -62 

+  0  -79 

6 

05-75 

-0-34 

6 

05  -60 

—  0  -19 

4 

05-65 

-0-24 

6 

04  -66 

+  0  -75 

4 

05-89 

—  0-48 

6 

04  -83 

+  0  -58 

4 

04-56 

+  0-85 

6 

05  -48 

—  0-07 

4 

05-14 

-f-o  -27 

4 

g6  -62 

—  1   -21 

4 

05-52 

^G-II 

4 

05  -00 

+0-41 

3 

05  -23 

+0-18 

4 

05  -84 

-0  -43 

4 

05  -29 

+0  -12 

4 

06  -29 

~o  -88 

6 

04  '93 

+0  -48 

4 

06  -33 

— 0  -92 

4 

06  -70 

-[  -29 

6 

04  -84 

+0-57 

Indi.scriminate  mean  =40°  22'  o5'"-44. 
Weighted  mean  =40     22    05    -4i±o' 

,.  =±o"-82. 
81  observations,  24  pairs. 

[Reduction  to  A  =o"-oo.] 


■oS. 


t  Groouil^ridge. 


J  Greenwich  12  year  Cat.  1845. 


THK    ASTRONOMIC    MP:ASrRHS. 


291 


29.  )'ard,  Pennsylv;iiii;i 
1854.  One  division  of  level 
at  this  station. 


— J.    H.    Hilj(anl.     Zenith  telescope  No. 
=f)"'.S<),     One  tnrn  of  niicronieter=76''''i 


6.     October   17  to  November  2, 
5,  from  circiimpolar  obsevations 


I'airs  nl'  stars. 


I 
I 


I 


7  "29 

7  085 

*7  (.91 

7   "31 

*7  091 

7   132 

7   141 

7   144 

7   1.S2 

7   194 

7  213 

7  253 

7  260 

"7  297 

7  277 

"•■■7  297 

7  3'3 

7  326 

7  363 

7  372 

*7  399 

7  469 

*7  399 

7  480 

7  402 

7  462 

7  521 

7  554 

7  560 

7  607 

7  610 

7  674 

7  696 

*7  712 

7  69S 

-7  712 

7  727 

7  731 

7  757 

7  787 

7  805 

7  851 

7  878 

7  90>'^ 

7  937 

7  973 

7  984 

8  037 

8  059 

8   156 

8  082 

*8   159 

8   114 

*8  159 

8   177 

8    .87 

8  206 

8   231 

S  279 

S   299 

8  312 

8  3 '4 

8  355 

26 

32 

46 

60 

67 

80 

87 

114 

156 

i66 

180 

Adopted  seconds  of 
mean  N.  I'.  U. 

"' 

^l> 

l.atiUiiU. 

7' 

f  f 

// 

0        /          // 

// 

43  '69 

'3-97 

6 

13 

39  58  28  -58 

4-0  -81 

14  '03 

06  -40 

4 

6 

29-63 

— 024 

14 '03 

02-45 

4 

6 

29-98 

-0  59 

29  "97 

(;9  -66 

3 

6 

2916 

fo-23 

58 -3  > 

39-23 

8 

17 

29-63 

—0  -24 

38-34 

49-23 

4 

9 

29  -60 

— 0-2f 

02  '53 

01  -90 

4 

6 

29-46 

—  0  -07 

34-06 

01  -90 

6 

9 

30-04 

-0-65 

5378 

4971 

I 

2 

29  •90 

-0-51 

II  -25 

56-30 

4 

9 

■       28  -54 

+  0-85 

50-15 

02-33 

1 

1 

29-40 

— o-oi 

50-15 

05  -90 

6 

9 

29  54 

-0-15 

59  78 

57 -oi 

5 

II 

29-66 

-0-27 

24-76 

21  -7,S 

4 

9 

29-36 

+0-03 

30-78 

13-72 

5 

II 

28-64 

+0-75 

31-90 

00  -40 

4 

9 

29  39 

0-0() 

31  -90 

21  '34 

4 

6 

29-53 

—  0-14 

24-82 

21  -34 

4 

6 

28  -83 

+0-56 

46  -90 

10-96 

4 

9 

28-36 

-ri  03 

51  -26 

27-72 

6 

'3 

30-54 

-1  -'5 

26-30 

45-57 

6 

13 

29  20 

+019 

45 '53 

46  02 

2 

4 

29-08 

+0-31 

05-55 

44-06 

5 

1 1 

29-72 

-0-33 

01  -43 

43-56 

2 

4 

30  57 

-I  -iS 

56-11 

•5-'7 

5 

1 1 

30  -30 

—0-91 

26  •!() 

59-20 

2 

3 

29  29 

-f-o-io 

54  -80 

59-20 

5 

7 

29-51 

— 0-12 

20-32 

43 -'3 

5 

1 1 

29  40 

— 0  -0 1 

48-41 

u  -18 

4 

9 

28-78 

+o-6i 

47-96 

23-42 

5 

1 1 

29-57 

— u'lS 

27  -22 

07  -98 

2 

4 

29 -Si 

—  0-42 

50  -42 

41   42 

3 

6 

29  35 

-roo4 

19-17 

41  -97 

3 

6 

29-17 

+0-22 

II  -90 

23  95 

3 

6 

30-08 

—0-69 

25-14 

08  -70 

3 

6 

28-75 

+0-64 

14-77 

•8-54 

3 

6 

28 -30 

+  1  09 

19-38 

20  -5 1 

4 

9 

29-31 

+0-0S 

Indi.scriniinat 

e  mean  =39° 

58'  29" 

-41. 

Weivjhted  nie 

ui            =39 

58  29 

■39^0 

"  -06. 

<=±o"  -68 
148  observations,  37  pairs. 

[Rednction  to   .\  =0"  -on.] 


Ik 


' 


292 


THE    EASTERN    OBUOUE    ARC. 


For  the  abstracts  of  results  corresponding  to  the  astronomic  latitudes  of  the  fol- 
lowing stations,  numbered  from  30  to  53,  inclusive,  that  is,  for  stations  common  to  the 
transcontinental  arc  and  the  oblique  arc,  see  ' '  The  Transcontinental  Triangulation ' ' 
United  States  Coast  and  Geodetic  Survey  Special  Publication  No.  4;  Washington,  D.  C, 
1900.  The  final  sunmiary  of  the  results  for  latitude  includes  the  adopted  latitude  at 
these  stations: 

D.  C. 


30.  Principio,  Md. 

31.  Maryland  Heights,  Md 

32.  Pooles  Island,  Md. 

33.  Sugar  Loaf,  Md. 

34.  Dover,  Del. 

35.  Webb,  Md. 

36.  Soper,  Md. 

37.  Rockville,  Md. 

38.  Taylor,  Md. 

39.  Strasburg,  Va. 

40.  Cape  May,  N.  J. 

41.  Caiisten,  D.  C. 


42.  Naval  Observatory  (new) 

43.  Hill,  Md. 

44.  Naval  Observatory  (old),  D.  C. 

45.  vSeaton,  D.  C. 

46.  Coast  and  Geodetic  Snrvej'  Office,  D.  C. 

47.  Bull  Run,  Va. 
4S.   Marriott,  Md. 

49.  Cape  Henlopen,  Del. 

50.  Clark,  Va. 

51.  Elliott  Knob,  Va. 

52.  Charlottesville,  Va. 

53.  Long  Mountain,  Va. 


54.  y)/06>r^.  North  Carolina. — J.B.Baylor.     Zenith  telescope  No.  2.     First  series.     November  8  to 


December  6,  1876.     One  division  of  level=i' 
polar  observations  at  this  station. 


'■06.     One  turn  of  micronieter=44'''"S57  from  circunu 


Pairs  of 

Stars, 

7  943 

7 

973 

8  068 

8 

071 

8   107 

8 

146 

8  171 

8 

206 

8  245 

8 

256 

7 

26 

100 

109 

130 

153 

219 

264 

318 

349 

388 

438 

456 

476 

518 

568 

595 

615 

656 

661 

740 

79' 

796 

S27 

863 

903 

9^5 

953 

981 

1 

017 

1  030 

1 

057 

I    OQQ 

J 

126 

Adopted 
mean 

seconds  of 
N.  P.  D. 

11' 

7V 

// 

// 

44  '53 

43-67 

7 

3 

54-41 

58-9' 

6 

3 

18  72 

01  '91 

6 

3 

12  -67 

32.  56 

7 

3 

42  TO 

29-75 

5 

2 

02  79 

21  -38 

9 

3 

28-90 

55  -78 

7 

3 

19  '20 

08  -34 

6 

3 

32-13 

oS  -30 

7 

3 

08  '41 

09-42 

6 

3 

19  '60 

28-61 

6 

3 

rg  -26 

2i  -30 

6 

3 

26  -68 

31  -CO 

7 

3 

45-44 

48-21 

8 

3 

0044 

47-9' 

6 

3 

23  -64 

07-52 

4 

2 

34  -62 

52-24 

5 

2 

'4  -63 

20  -50 

7 

3 

57  -00 

28-81 

7 

3 

39  -36 

01  -35 

6 

3 

37  -46 

31  -60 

7 

3 

19-53 

24  -60 

6 

3 

Latitude. 


36   23 


55-62 

-0  -54 

55  -67 

-0-59 

53  -85 

+  1  -23 

54-87 

4-0  -21 

54-88 

'|-o  -20 

54-29 

+0-79 

55  -65 

-0-57 

55-84 

-0  -76 

54-63 

+0-45 

55-27 

—0  -19 

56  ■■6 

—  J  -08 

55  -18 

—0  -lo 

54 -89 

+0-19 

55  -16 

-0  -08 

54-99 

-1-0  -09 

56-87 

- 1  -79 

55  -89 

-o-8i 

56  -73 

i-65 

53  -/o 

^-1-38 

53  -59 

-1- 1  -49 

53  -84 

l-i  -24 

54-97 

+0  -II 

Indiscriminate  niean=36°  23'  55"-i2. 
Weighted  mean  =36     23    55    -o8±o''"i3. 

,.=  ±i''-o6. 
140  observations,  22  pairs. 

[Reduction  to  /i:,= — o"-o4.] 


THE    ASTRONOMIC    MEASURES. 


293 


I 


54.  Afoore,  North  Carolina. — W.  B.  Fairfield.  Zenith  telescope  No.  2.  Second  series.  Novem- 
ber 23  to  December  6,  1876.  One  division  of  level  =  i''()6.  One  turn  of  mi<ronieter=44"'S67  from 
circuinpolar  observations  at  this  station. 


fairs  of 

st.-irs. 

7  943 

7  973 

8  068 

S  071 

8   107 

8   146 

8   171 

8  206 

8  245 

8  256 

7 

26 

100 

109 

130 

153 

219 

264 

318 

349 

388 

438 

456 

476 

518 

568 

595 

615 

656 

66 1 

740 

791 

863 

903 

915 

953 

98 1 

I  017 

I  030 

I  057 

I  099 

I   126 

Adopted 
mean 

second.s  of 
N.  I>.  D. 

u' 

// 

// 

44  -53 

43-67 

6 

54-41 

58 -9  r 

6 

1872 

01  -91 

5 

12-67 

32  -56 

6 

42  •!() 

29-75 

6 

0279 

21  -38 

6 

28  -90 

55  -78 

6 

19    20 

08  "34 

6 

32-13 

08  -30 

6 

08-41 

09-42 

6 

19 '60 

28 -6  r 

6 

19    26 

23-30 

7 

26-68 

31  -oo 

7 

45-44 

48-21 

6 

00  "44 

47-91 

5 

23-64 

07-52 

6 

■4-63 

20-50 

6 

57-00 

28-81 

6 

39-36 

01  -35 

6 

37-46 

31  -60 

6 

19  -53 

24-60 

6 

w 

Latitude. 

V 

0     /          // 

// 

3 

36   23   56-04 

—  I  -22 

3 

55-14 

-032 

3 

53  95 

+  0  -87 

3 

55-13 

-0-31 

3 

54  -87 

—  0  05 

3 

53  -82 

+  1  "OO 

3 

55  -55 

-073 

3 

55-41 

-0-59 

3 

52  76 

+2-06 

3 

55-4' 

-0-59 

3 

54  -86 

—0-04 

3 

55  -69 

-0  -87 

3 

53  -58 

+1  -24 

3 

54-50 

+0-32 

3 

55  -21 

-0-39 

3 

56-47 

-1-65 

3 

54-90 

— 008 

3 

54-03 

-fo-79 

3 

55  37 

-0-55 

3 

53-76 

+  1  -06 

3 

54-74 

+o-o8 

Indiscriminate  mean  =36°  23'  54"-S2. 
Weighted  mean  =36    23    54    •82±o"-i3. 

c=±o"-e~. 
126  observations,  21  pairs. 

[Reduction  to  A,  =  — o''''-o4.] 
adopted  value  =36°  23'  54'"-95d=o"-09. 

[Reduction  10^;^  =  — o"-o4.] 


294 


THE    EASTERN    OBLIQUE    ARC. 


55.  Yohug,  North  Carolina. — H.  W.  Blair.  Zenith  telescope  No.  4.  First  series.  October  14 
to  21,  1876.  One  division  of  level  =  2"'2o.  One  turn  of  :nicronieter=43"'388  from  circuinpolar 
observations  at  this  station. 


Fairs 

of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

n' 

"£/ 

Latitude. 

V 

// 

// 

0      / 

// 

// 

6   S56 

6 

S58 

21   -95 

36  -45 

6 

2 

35  44 

22  -88 

- 1  -35 

6  962 

6 

966 

3T  '57 

oSt5 

5 

2 

22  -90 

-1  -37 

7  022 

7 

029 

20  -95 

32-26 

6 

2 

2  1  -63 

—  Q-IO 

7   174 

7 

194 

35  '03 

55  '55 

6 

2 

20  -68 

-0-85 

7  253 

7 

256 

53  -oS 

46-94 

6 

2 

20  -27 

-l-I   -26 

7  399 

[■ 

909] 

21  '60 

45 --S I 

6 

2 

23  -20 

-1-67 

7  465 

7 

521 

59  'og 

33  74 

6 

2 

22-88 

-I   -35 

7  5S5 

7 

59S 

20  •17 

49-61 

6 

2 

20-50 

t    I  -03 

7  712 

7 

746 

GO  •  1 2 

20  -3 1 

6 

2 

20  -36 

^I   -17 

7  914 

7 

972 

20  -45 

46-74 

6 

2 

21  -36 

-;  0-17 

8  082 

8 

160 

15  -54 

41  -38 

5 

2 

20  -84 

-1  0  -69 

8  114 

8 

131 

43  -23 

17-15 

5 

2 

2<J  -35 

-i-i  -18 

8   195 

8 

211 

41  '56 

17-48 

5 

2 

21   -28 

'  0-25 

8  229 

8 

256 

05  -86 
Indiscriminate 

29-75 
mean  = 

=35^ 

5 
44'  21" 

2 
■53- 

22-23 

—0  -70 

Weighteil  mean          = 

=35 

44    21 

•53± 

0''-20. 

f= 

=  ±o''-67. 

79  ob.servation 

s,  14  pairs. 

[Reduction  to  A=+o"-oi.] 

55.  Voitng,  North  Carolina. — J.  B.  Boutelle.  Zenith  telescope  No.  4.  Second  series.  October 
24  to  31,  1876.  One  division  of  level  =  2"-2o.  One  turn  of  micronieter=43"-388  from  circumpolar 
observations  at  this  station. 


Pairs  of  stars. 


7  664 

7  961 

8  153 
8  203 
8  370 

28 
120 
198 
244 
2S3 
395 
4S8 
558 
628 


7  755 

7  975 

8  182 
8  231 

7 
[20] 

173 
215 
269 

345 
404 

515 
592 
675 


Adopted  seconds  of 
mean  N.  P.  D. 


22  -67  49  -24  6 

17  -66  56  -80  6 

46  -26  23  -So  6 

06-13  54  -25  6 

37-17  02-79  6 

57-40  15-97  6 

10-57  19-13  6 

40-18  27-77  6 

57  -98  30  -o(3  6 
18 -68  08 -80  6 
17-46  1 8  -60  6 

34-53  31  -1'  6 
04-50    17-70      6 

58  -85    44  -30      6 

Indiscriminate  mean  =  35°  44'  21^-47. 
-Weighted  mean  =35    44    21      47  ±  o"-i5. 

e—±o"  -64. 
84  observations,  14  pairs. 

[Reduction  to  A  =  +o"-oi.] 
Adopted  value  =  35°  44'  2i''-5o  rt  o'''-i2. 

[Reduction  to  /t\  =4-o"-oi.] 


lU 

I.atitnde. 

'" 

0      /          // 

// 

3 

35  44  21  -34 

:  0-13 

3 

20-95 

:  0-52 

3 

21   -'05 

-i-o  -42 

3 

21   -45 

-^-o  -02 

3 

23  -26 

"  1  -79 

3 

22  -18 

—0  -71 

3 

22  -05 

^^-0  -58 

3 

22  -61 

-  I  -14 

3 

21    -07 

■  0  -40 

3 

20  -58 

-  0  -89 

3 

20-77 

-i  0  -70 

3 

21  -68 

—  0  -21 

3 

20  -41 

:  I  -06 

3 

21   -17 

^t-0-30 

THE   ASTRONOMIC   MEASURES. 


295 


56.  h'iiii^.  North  Carol 
13,  1S76.  One  division  of  k- 
tions  at  this  station. 


ina.— H.  \V.  lilair.     Zenith  telescope  No.  5.      First  series.     Ueceniber  5  to 
vel=o"-9,S.     Oni-  turn  of  micrometer  =ii"-42o  from  circumpolar  observa- 


I'air.s 

)f  stars. 

.\(loi)lecl  seconds  of 
mean  N.  P.  I). 

n' 

7v               Katitu 

de. 

V 

// 

// 

0       / 

// 

ff 

S  052 

8  fJ5S 

n2  -66 

55-58 

5 

5      35  12 

3  '37 

-o-ii 

S   125 

S  160 

17-61 

41 -.38 

5 

5 

2-56 

-r0  7o 

S  206 

S    212 

32  -56 

48  -85 

5 

5 

'3-34 

-008 

8  26: 

8   324 

05  -06 

51  -04 

5 

5 

3-92 

-0-66 

S345 

4 

23  '3" 

38-41 

5 

5 

4-17 

-^0-91 

67 

120 

05  -85 

'0-57 

5 

5 

3-38 

—012 

170 

180 

31   -20 

05-37 

5 

5 

2  -60 

+0-66 

218 

269 

33 '05 

30-00 

5 

5 

2-39 

-fo-87 

330 

365 

1 1  -58 

22  -90 

5 

5 

4-19 

-093 

456 

488 

19-26 

34  -53 

5 

5 

3-10 

-fo-i6 

522 

577 

■3  '"5 

56-04 

5 

5 

2  -90 

+0-36 

649 

698 

47-89 

37  -60 

5 

5 

4  06 

-  o-So 

727 

759 

02  -43 

38  -34 

5 

5 

3  -85 

-0-59 

813 

829 

19-96 

53  •73 

5 

5 

■3-97 

-0-71 

885 

901 

48  -09 

18  -50 

5 

5 

3-24 

-r0  02 

94  r 

967 

46-75 

50  -22 

5 

5 

3-37 

— o-ii 

999 

I  007 

58  -94 

02-63 

5 

5 

3  -61 

-0-35 

I  034 

I  043 

05-15 

55  -9" 

5 

5 

2-43 

+0-83 

I  058 

I  084 

37-11 

26  -24 

5 

5 

2  -60 

+0-66 

I    117 

I   J74 

01  72 

24  TO 

5 

5 

2  -20 

-t-I  -06 

Indiscriniin 

ate  mean 

=35° 

12' 

i3"-26. 

Weighted  mean 

=35 

12 

13    -26±o"-io 

(' 

=  d=C 

/'-31 

• 

100  observations,  20  pairs. 

[Reduction  to 

A  = 

-ri6"-o7.] 

296 


THE   EASTERN   OBLIQUE   ARC. 


56.  /\'i>ig.  North  Caroli 
12  to  20,  1876.  One  division 
tions  at  this  station. 


na. — J.  B.  Boutelle.     Zenith  telescope  No.  5.     Second  series.     December 
of  level=o"'98.     One  turn  of  micronieter=4i"'56i  from  latitude  ohserva- 


Pairs  of  stars. 

AQoptea 
mean 

seconas  01 
N.  P.  D. 

//' 

W 

Latitude. 

V 

// 

// 

0       / 

" 

// 

8  256 

t4   172 

2975 

54 '74 

5 

4 

35   12 

13  -39 

—0-02 

8  364 

8  370 

30-10 

37-17 

5 

4 

13-24 

+0-13 

26 

92 

21  -38 

43-09 

5 

4 

14-25 

—0  -88 

lOI 

153 

37-13 

08-34 

5 

4 

14  -22 

-0  -85 

178 

189 

03  -04 

13  -57 

5 

4 

14-34 

-0-97 

198 

264 

40-18 

08-30 

5 

4 

13-62 

-0-25 

283 

349 

1 8  -68 

09-42 

5 

4 

14-08 

-0-71 

515 

561 

31  -11 

18 -20 

5 

4 

12-39 

+0-98 

569 

628 

34  -25 

58  -85 

5 

4 

12-43 

+0-94 

682 

735 

21  -44 

03-14 

5 

4 

12-58 

+0-79 

769 

7S5 

46-25 

56-30 

5 

4 

12  -69 

+0-6S 

842 

863 

51  -60 

14-63 

5 

4 

13  -32 

+0-05 

904 

912 

59 '45 

05-47 

5 

4 

13-62 

-0  -25 

947 

966 

51  -12 

59-89 

5 

4 

12  -20 

4-1  -17 

983 

I  025 

37-96 

09-77 

5 

4 

14-40 

-I  -03 

I  069 

I  099 

29-64 

19-53 

5 

4 

12  -70 

+0  -67 

I   123 

!     132 

17-54 

03-57 

5 

4 

14-30 

-0  -93 

I   155 

I    210 

32-ri 

41  -87 

5 

4 

13-26 

+0  -I  I 

I  289 

I    287 

25  -64 

29-74 

5 

4 

13-05 

+0  -32 

1  301 

I    311 

42  -80 

43-20 

5 

4 

13-40 

-0-03 

Indiscriminate  mean      = 

=  35° 

12'  13" 

-37- 

Weighted 

mean               = 

e  = 

■35 

±0 

12    13 

"•34. 

•37±o" 

II. 

100  observations,  20  pairs 

[Reduction  to  A  = 

+  i6''-o7.J 

Adopted  value                 = 

35° 

12'  13" 

■3i±o" 

07. 

[Reduction  to  A  = 

=+i6"-o7.] 

t  Groombridge. 

THE   ASTRONOMIC   MEASURES. 


297 


57.  Paris,  .South  Carolina. — J.  B.  Boutelle.  Zenith  telescope  Xo.  5 
I7>  •'^VS-  One  division  of  level=o""944.  One  turn  of  niicronu'ler=4i"5 
at  this  station. 


First  series.     October  4  to 
14  from  latitu'le  observations 


Fairs  of  .stars. 


6  810 
6  876 

6  941 

7  029 

*7  103 
7  152 
7  200 
7  271 
7  44« 
7  512 
7  554 
7  664 
7  731 
7  798 
7  888 

7  914 

7  972 

8  052 
8  182 
8  206 
8  227 
8  2S0 


6  830 

6  882 

7  007 
7  061 

■■•7' 103 

7  '5S" 
7  262 

7  377 
7  450 
7  520 
7  607 
7  683 
7  777 
7  «5o 
7  900 

7  932 

8  032 
8  056 
8   1 88 

■  8  212 
8  252 
8  3CX5 


Adopted  seconds  of 
mean  N.  P.  D. 

n' 

7V 

Latitude. 

T 

// 

// 

0      /         // 

// 

22  '04 

24-52 

5 

5 

34  56  3'  -6" 

+  046 

04-16 

42-50 

6 

5 

33 -'3 

-I   -07 

08  -57 

35  -26 

6 

5 

32-61 

-0-55 

43  72 

10  -03 

5 

5 

33-00 

-0-94 

35  32 

35  -32 

5 

3 

31  -44 

+  0-62 

10 -61 

41  -85 

5 

5 

3'  -08 

+  0-98 

29 '45 

45  '40 

5 

5 

31  -'o 

+  0-96 

31  -86 

37-85 

5 

5 

30-63 

+  1    -43 

47  "08 

53-92 

5 

5 

32  30 

—  0-24 

29-36 

33-53 

5 

5 

31   93 

+0-I3 

42  -05 

24-88 

5 

5 

32  44 

-0-38 

40-76 

07-67 

5 

5 

32-38 

-0-32 

04-25 

22  -80 

5 

5 

33-06 

—  I  00 

54  74 

00-34 

6 

5 

32-21 

-0-15 

58-00 

09  -09 

5 

5 

32  -73 

—0  -67 

40-15 

10-15 

6 

5 

32-33 

-0-27 

05  77 

41  -03 

5 

5 

31-57 

-fo-49 

22  -06 

26-86 

5 

5 

3'  -71 

+0-35 

43  65 

23  -73 

6 

5 

31  -90 

+o-i6 

52  -60 

08-68 

6 

5 

32-18 

—0-12 

29-70 

26-95 

5 

5 

31  -90 

+0-16 

57  77 

53  -55 

5 

5 

31  -77 

4-0  29 

Indiscriminate  mean  =34°  56'  32^-05. 
Weighted  mean  =34     56     32    -o6rto'''-io. 

c=±o"-T,6. 
116  observations,  22  pairs. 

[Reduction  to  A,  =  — o''''-87.] 


. 


298 


THE    EASTERN    OBLIQUE    ARC. 


57.  Paris,  South  Carolina. — H.  W.  Blair.  Zenith  telescope  No.  5.  Second  series.  October  iS  to 
25.  '875.  One  division  of  level  =  o"  944.  One  turn  of  micrometer  =  41" -386  from  circnmpolar 
observations  at  this  station. 


Pairs  of  stars. 


7    204 

7  260 
7  437 
7  495 
7  606 

7  674 
7  7:vS 
7  807 

7  871 
S  003 
S  028 

8  099 
8  261 
8  345 

82 

]02 
189 
226 

*334 
339 
416 
470 


7  213 
j-2  065 
7  455 
7  553 
7  64? 
7  696 
7  796 
7  855 

7  912 

8  or3 
8  097 
s  171 
8  324 

4 
92 
I  21 

215 
250 

*334 
370 
454 
508 


idopted  seconds  of 
mean  N.  P.  D. 

// 

// 

49-16 

•13  -74 

19-40 

53-66 

41  -or 

34-65 

28  -93 

4:  -30 

40  -50 

32  -40 

59  'PS 

27  -52 

37  -82 

26  -07 

58-19 

35  -56 

17-85 

07-72 

19-56 

16-54 

5"  -74 

58  -93 

14  -18 

32-48 

25  "03 

1 1  09 

43  '34 

58-21 

37-80 

03-14 

25-44 

05  -15 

33-37 

47-45 

01  -QI 

55  -02 

33  -49 

33  '49 

56-08 

44-07 

55  -oo 

21  -54 

54  -50 

18 -61 

5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 

Indiscriminate  mean  =  34°  56'  3 

Weighted  mean  =34     56    3 

e  =  ±  o"-27. 

no  observations,  22  pairs. 

[Reduction  to  A  =   -o."87.] 

Adopted  value  =34°  56^31 

[Reduction  to  A  =  —  o-''87.] 


w 

I,atilude. 

V 

0       / 

// 

'/ 

6 

34  56 

31  -57 

+0-29 

6 

32  -02 

—0  -16 

6 

32  -68 

~o  -82 

6 

31  -30 

+0-56 

6 

31  -56 

+0-30 

6 

31  -72 

^-o  -14 

6 

3'  -70 

+0-16 

6 

30  -88 

+0-98 

6 

31  -32 

+0-54 

6 

32-21 

-0-35 

6 

3'  -57 

-I-0-29 

6 

32-54 

-0-68 

6 

32  -06 

—0  -20 

6 

32  -06 

— 0-20 

6 

.^2  -39 

-0  -53 

6 

31  -92 

—  0  -06 

6 

32  -03 

-0-17 

6 

32-71 

-0-85 

3 

33  -33 

-1-47 

6 

30-99 

+0-87 

6 

30  -90 

+0-96 

6 

32-13 

—0  -27 

i" 

■88. 

I 

-86  rfc  0" 

-oS. 

-96  ±o"'07. 


tKadcliffe  Catalogue. 


THE    ASTRONOMIC    MKASIRKS. 


299 


58.  Currahcc,  Georgia.  H.  \V.  Blair.  /Aiiith  tck-sc(jpe  Xo.  5.  I'irst  series.  September  2S  to 
October  8,  1874.  One  division  of  level  =  o"'94  from  observations  at  this  station,  (^ne  turn  of 
micrometer  =  4i'''''38i  from  circumpolar  ob.servations  at  this  station. 


I'air.s  0 

f  .stars. 

6  571 

6  599 

6  637 

6  656 

6  697 

6  739 

6  764 

6  794 

6  824 

6  839 

6  858 

6  895 

6  944 

6  963 

*6  998 

*6  998 

7  008 

7  067 

7  094 

7   105 

7  215 

7  257 

7  275 

7  301 

7  350 

7  377 

7  402 

7  444 

7  474 

7  480 

7  528 

7  548 

7  606 

7  612 

7  641 

7  683 

7  705 

7  706 

7  807 

7  820 

7  855 

7  856 

7  9'5 

7  923 

7  953 

8  003 

8  023 

8  032 

8  076 

8  079 

8  097 

8  128 

S   158 

8   182 

8  250 

8  280 

Adopted 
mean 

seconds  of 
N.  I'.  D. 

h' 

w 

I,;ititiule. 

V 

// 

// 

0      /         // 

// 

31  74 

22  -34 

5 

5 

34  31   37-32 

-i-o-43 

40  -03 

22-44 

5 

5 

38  -05 

—0-30 

"6  54 

26  -40 

5 

5 

38-32 

-0-57 

26-47 

20-20 

5 

5 

37-73 

+0-02 

51  -47 

49  -75 

5 

5 

37-53 

4-0-22 

54  76 

42  24 

5 

37-60 

+  0-15 

45-15 

08  -25 

6 

37  -64 

+0-1 1 

35-87 

35  -87 

5 

38  -33 

-0-58 

35 -'7 

02  -5 1 

5 

38  -03 

-0-28 

10  -28 

49  94 

5 

38  -46 

-0-71 

18 '44 

40-94 

5 

38  -50 

-0-75 

35  -60 

12-52 

5 

38-09 

-0-34 

29-42 

52-53 

5 

36-15 

-1  -60 

00  -J,}, 

01  -55 

5 

36-19 

-■•56 

43-96 

51-78 

5 

38-29 

-054 

oS-14 

17-84 

5 

36-64 

-pi  -11 

57-'2 

25-68 

5 

37-30 

+0-45 

13  -87 

24-94 

5 

38  - 1 2 

-0-37 

54-13 

10-13 

5 

36-97 

+0-78 

16-25 

43-26 

5 

37-22 

+0-53 

53  -84 

06-71 

5 

38  -05 

-0-30 

56  -37 

13  -32 

5 

37-81 

— o-o6 

51  -15 

38-76 

5 

38-41 

-0-66 

01  -48 

00  -52 

5 

38-59 

— 0-S4 

55  -39 

57  -83 

5 

38  -55 

— o-So 

18-56 

40  -85 

5 

38  -29 

-'>  54 

21    79 

03  -5" 

5 

37  -36 

*  0  -39 

03  -95 

17-82 

5 

37  60 

+o-'5 

scriminate  mean  =  34° 

3>'  37" 

-75- 

^hte<l  mean            =  34 

3 '     37 

•75 

±o"-o9. 

,■=  ±o"-32. 
141  olxservations,  28  pairs. 

[Reduction  to  A  =+  6" -21 


300 


THE    EASTERN    OBLIQUE    ARC. 


58.  Cnrrahcc,  Oeorgxa.. — J.  B.  Boutelle.  Zenith  telescope  No.  5.  Second  series.  October  12  to  21, 
1874.  One  division  of  level  =  o'''''94  from  observations  at  this  station.  One  turn  of  micrometer 
=  4i"'3Sr  from  circumpolar  observations  at  this  station. 


Pairs 

af  .stars. 

6  754 

6  827 

6  868 

6  88r 

6  957 

7  027 

7   174 

7  256 

4  502 

7  326 

7  37^ 

7  3>^7 

7  437 

7  561 

7  565 

7  623 

7  674 

7  71S 

7  749 

7  796 

7  .S25 

7  900 

7  912 

7  961 

8  052 

8  no 

8  136 

8  159 

8  299 

8  307 

7 

14 

dopted 
mean 

second.s  of 
N.  1'.  D. 

;/' 

IV 

Latitude. 

V 

// 

" 

0      /          // 

// 

22  -53 

51  -94 

5 

3 

34  31   37  -06 

+0-65 

31  "94 

21  -70 

5 

3 

37-31 

+0-40 

09-44 

32  •21 

5 

3 

37 -87 

—0  '16 

00-45 

14  -00 

5 

3 

36-94 

+0-77 

13  '63 

08  -54 

5 

3 

37  -62 

Ho  -09 

08-66 

18  -50 

5 

3 

37-70 

+0-01 

56  '30 

15 '3' 

5 

3 

37  -53 

+o-i8 

I  2  -59 

42-42 

6 

3 

36-88 

+0-83 

16-28 

25-96 

5 

3 

37-90 

—0  '19 

10  -35 

44  -[2 

6 

3 

37  -72 

—0  -01 

18-79 

26-68 

5 

3 

36  -93 

+0-78 

26  -43 

55-62 

5 

3 

37-19 

+0-52 

41  '45 

15  -02 

5 

3 

39-61 

—  I  -90 

iS  -26 

24-47 

5 

3 

38  -77 

—  I  -06 

45 '87 

43  -29 

5 

3 

39  -37 

-I  -66 

42-54 

20-15 

5 

3 

37-00 

+0-71 

Indiscriminate  mean  =  34°  31'  yi"'1\. 
-Weighted  mean  =34    3^    37    -71 

f  =  =b  o"-49. 
82  observations,  16  pairs. 

[Reduction  to  A  =  +  6"-2i.] 
Adopted  value  =34°  31'    37''-75 

[Reduction  to  A  =  ^b"-2\.'\ 


±  o"-i4. 


:o"-oS. 


t  Armagh,  1840. 


'I 


thp:  astronomic  measures. 


301 


59.  Lavender,  Georgia. — F.  P.  Webber.     Zenith  telescope  No.  3.    October  20  to  November  4,  1874. 


One  division  of  levels i^^'20. 
tions  at  this  station. 


One  turn  of  niiiTonieter=46'''''6a  deterniint 


I'airsof 

star.s. 

Adopted 
mean 

seconds  of 
N.  P.  I). 

h' 

7V 

// 

// 

7  310 

7 

350 

1279 

29-42 

8 

3 

7  553 

7 

582 

57  -49 

49-75 

6 

3 

7  607 

7 

614 

41  -5' 

09  -32 

5 

3 

7  643 

7 

664 

07  •  1 2 

56  •90 

5 

3 

7  712 

7 

729 

34  '99 

56-79 

6 

3 

7  S20 

7 

856 

43  '26 

06  -71 

7 

3 

7  ''^79 

7 

923 

29 '57 

13  -32 

5 

3 

7  997 

8 

059 

22-27 

25  -08 

6 

3 

8  097 

8 

118 

17-90 

50  -3" 

5 

3 

8   r49 

8 

'5S 

33  -Si 

21  -79 

5 

3 

8  2S2 

8 

300 

12-56 

13-53 

5 

3 

79 

lOI 

42-48 

17-29 

5 

3 

121 

156 

25-11 

40-70 

5 

3 

180 

214 

44-91 

36-50 

5 

3 

305 

339 

55-35 

15-39 

5 

3 

377 

395 

30-80 

55-68 

S 

3 

560 

572 

5273 

20  -70 

6 

3 

587 

644 

13-00 

II  -68 

5 

3 

7  559 

7 

568 

50  -89 

32-05 

5 

-« 
0 

7  641 

7 

668 

13-87 

39  22 

5 

3 

7  855 

7 

900 

53-84 

26  -68 

5 

3 

7  962 

8 

032 

47-41 

00-52 

6 

3 

S  058 

8 

131 

34-35 

56-50 

5 

3 

8  160 

8 

224    • 

21  -00 

27-85 

7 

3 

142 

169 

16-58 

14  -So 

5 

3 

219 

247 

1  r  -45 

40-63 

5 

3 

321 

343 

38  -90 

47-53 

6 

3 

Indiscriniin 

ate  inean  = 

34" 

19'  15'' 

•81 

"Weighted  mean          = 

34 

'9    15 

-Si 

('= 

=  =bO 

"■65. 

151  observations,  27  pairs. 

[Reduction  to  A 

=  + 

i''-24.] 

Latit 


34   19 


:0"-I2. 


1  from  latitude  observa- 


ide. 
// 
6  -41 
6-67 
6-12 
6  02 
4-73 
4-87 
4-45 
5-62 
7-32 

6  -oS 

5-65 
7-15 
6-17 
5-14 
4-73 
6-51 
4-42 
7-40 
5-70 

7  -22 

5 -58 
6-25 
4-58 
5-88 
6  -07 
5-56 
4-55 


— o  -60 
-0-86 
—0-31 

— O  -21 

+  1  -08 

-fo-94 
+  1-36 
+0-19 

-I  -51 
—0-27 
+0-16 
-I  -34 
—0-36 
+0-67 
+  1  -oS 
—0-70 
+ 1  '39 
-1  -59 
4  o  -II 

-  1  -41 
+0-23 
-0-44 

+  1  -23 
— o  -07 
— 026 
+0-25 
-M-26 


302 


THE    EASTERN    OBLIQUE    ARC. 


60.  Sa 

ivnee, 

Georgia 

One  division  of 

levels  I 

this  statioi 

1. 

Pairs  c 

f  stars. 

6 

583 

6  644 

*6 

698 

*6  698 

6 

723 

6  739 

6 

762 

6  769 

6 

779 

6  827 

6 

805 

6  867 

6 

S39 

6  S56 

6 

88 1 

6  896 

6 

890 

6  928 

6 

975 

6  983 

7 

006 

7  029 

7 

055 

7   ■■07 

7 

143 

7   i7t 

7 

1 88 

7  241 

7 

257 

7  281 

7 

310 

7  351 

7 

368 

7  398 

7 

474 

7  501 

7 

5.53 

7  5«2 

7 

607 

7  614 

7 

641 

7  668 

7 

712 

7  727 

7 

820 

7  806 

7 

882 

7  900 

7 

923 

7  931 

7 

945 

7  95« 

,  — H.  W.  Blair.     Zenith  telescope  No.  5.     First  series.     October  6  to  17,  1873, 
''•QO.     One  turn  of  niicronieter=4r"'429  from  circutnpolar  observations  at 


Adopted 
mean 

seconds  of 
N.  P.  D. 

// 

// 

23-20 

31  -63 

57  '40 

57  -40 

03-41 

34-50 

02  -04 

50-67 

41  -98 

01  -14 

02  -QO 

33  -66 

59 ''3 

50-15 

29-63 

03-28 

25-31 

32  -49 

21  '39 

29  -70 

58  '44 

06-66 

52-05 

44-24 

41  -57 

21  -34 

56-99 

05-54 

55-52 

03-05 

2674 

04-85 

34-57 

12-15 

00-25 

3'  -'6 

'3-72 

06  -17 

58-14 

26  -05 

3' -36 

56-41 

52  -43 

14  -32 

01  -40 

25-13 

I  [  -16 

45-36 

32-07 

57  -97 

07-43 

06  -07 

Latitude. 


9 

5 

10 

9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 


34 


4  04-14 

+0-26 

04  -QO 

+0-40 

05  -35 

-0-95 

03-91 

+0-49 

03-62 

+0-7S 

03-25 

+  1-15 

05  -10 

—0  -70 

04  -18 

+0-22 

03  -65 

+0-75 

04-47 

— 0  -07 

04-18 

+0-22 

04-69 

—0  -29 

04  -43 

—0-03 

04-73 

-0-33 

04-76 

-0-36 

03  -5« 

+0-82 

04  -84 

-0-44 

04  -62 

-0  -22 

04  -02 

+0-38 

04  -63 

-0-23 

05-32 

— 0  -92 

04  -20 

+  0-20 

04-13 

+  0-27 

04-67 

-0-27 

04-37 

+0-03 

05-22 

-0  -82 

Indiscriminate  mean=34°   14'  04^-39. 
Weighted  mean  =34     14    04    -4o±o"-o7. 

(•=±o"-28. 

132  observations,  26  pairs. 

[Reduction  toA=+6"-89.1 


THE   ASTRONOMIC   MEASURES. 


303 


60.  Sazvficc,  Georgia. — A.  H.  Scotl,  /enitli  telescope  No.  5.  Second  series.  October  30  to  Novem- 
ber 15,  1873.  One  division  of  level  =  i" 'cxj.  One  turn  of  niicronuter  =41"  •  129  from  circumpolar 
observations  at  this  station 


Pairs  of  stars. 


7  137 
7  306 
7  3«o 
7  559 
7  59" 
7  674 
7  S55 

7  913 

8  114 
8  282 

92 
164 
224 

305 
352 


7  166 
7  36' 
7  449 
7  568 
7612 

7  749 
7  «93 

7  958 

8  146 
8  300 

142 
181 
227 
3 '4 
365 


adopted  stfcoiuls  of 
mean  N.  P,  IJ. 

//' 

7V 

I,.-Uitude. 

V 

>' 

" 

0       /         // 

// 

45  •9" 

3" '31 

5 

4 

34   14  "3  •'•"5 

+  0-30 

32  '55 

14 -(17 

5 

4 

04  -61 

—0-46 

33  ^V 

04  -16 

5 

4 

04  -26 

— o-ii 

07-17 

48-19 

5 

4 

03-79 

+0-36 

30  '.So 

42  -39 

6 

4 

04-23 

-o-o8 

33 '52 

27-99 

6 

1 

03  53 

+0-62 

12  23 

02-81 

6 

4 

04  -QI 

+0-14 

18 '59 

06  -26 

6 

4 

03-12 

+  1  -03 

42 -ir 

01   -QO 

5 

4 

04    12 

+0-03 

32-54 

33-50 

4 

3 

03-52 

+0-63 

43 ''4 

36  -50 

6 

4 

05-59 

-I  -44 

40-52 

22  -62 

6 

4 

05  -53 

-1-38 

23 '05 

47-09 

6 

4 

04-88 

-0-73 

14  -80 

'3 '77 

5 

4 

02-95 

-(-I  -20 

21  -iS 

20-62 

6 

4 

03-90 

-fo-25 

riminate 

mean  = 

34° 

H' 

04" 

-13- 

ited  mean           = 

=34 

14 

04 

i5zto' 

'•14. 

e= 

:±o" 

•51 

82  observations,  15  pairs. 

[Reduction  to  A  =  -f   6"  -89.] 
Value  adopted  =34°  14' 04" -20-11:0' 

[Reduction  to  A  =  +6"  -89.] 


-oS. 


304 

6i.  Aurora,  Alabama. - 
division  of  level  =  i "  '006. 
this  station. 


THE   EASTERN    OBLIQUE    ARC. 

-F.  P.  Webber.     Zenith  telescope  No.  2.     May  28  to  Jnne  20,  1877.     One 
One   turn  of  micrometer  =  45"  -852   from    circumpolar  observations  at 


Pairs 

of  stars. 

Adopted 
mean 

.seconds  of                  , 
N.  P.  D.                     " 

70 

Latitude. 

V 

// 

// 

0      /        // 

// 

4  057 

4 

127 

t8  '90 

15-10                 5 

3 

34  08  48  -72 

-1-27 

4  148 

4 

156 

59  '48 

38  -60              5 

3 

47-74 

—0  -29 

4  274 

4  305 

05  -20 

32  -60              5 

3 

46  -65 

+0-80 

4  335 

4 

367 

21  -00 

45  -50               5 

3 

47-59 

-0-14 

4  406 

4 

456 

10  '50 

15-22               5 

3 

46-90 

+0-55 

4  6S4 

4 

753 

09  -88 

43-18              6 

3 

46-49 

+0-96 

4  870 

4 

S76 

1073 

23  -05              6 

3 

48-73 

—  1  -28 

4  958 

4 

969 

2470 

18-32              6 

3 

48  -30 

-0  -85 

5  026 

5 

031 

25-07 

42  -24              5 

3 

49-43 

—  I  -98 

5  075 

5 

084 

00-52 

25  -75               4 

3 

46-56 

+0  -89 

5  130 

5 

143 

56  -38 

13  -00               5 

3 

46-94 

+0-51 

5  177 

5 

252 

46  -So 

03  -60               5 

3 

47-51 

—0  -06 

5  295 

5 

321 

48  -80 

13  -57               5 

3 

46-53 

+  0-92 

5  432 

5 

479 

43 'oi 

37  -63              5 

3 

46  -12 

+ 1  '33 

5  502 

5 

587 

53 '64 

53  -78              5 

3 

48-17 

—0  -72 

5  834 

5 

927 

04-50 

56- 25              5 

3 

47-11 

+0  -.u 

5  937 

5 

991 

25  -ID 

21-83              6 

3 

47  -36 

+0  -09 

6  091 

6 

094 

45  -85 

26  -60              5 

3 

49-32 

-I  -87 

6  151 

6 

203 

ID  -25 

54-18              5 

3 

48  -28 

-0  -83 

4  242 

4 

303 

44-50 

45  -85              5 

3 

46  -73 

+0-72 

4  597 

4 

701 

45 '45 

36  -44              5 

3 

47-56 

— Q-II 

4  751 

4 

845 

38  -25 

40  -23              5 

3 

47-47 

—  0  -02 

4  905 

4 

gSo 

16-66 

23  -48              5 

3 

47-14 

+0-31 

5  185 

5 

313 

24-14 

08  -06              5 

3 

47-11 

+  0  -34 

5  322 

5 

388 

10  -41 

30  -48              5 

3 

46  -80 

+  0-65 

5  463 

5 

525 

34  73 
Indiscrimin 

27  -79              5 
ate  mean  =  34°  08' 

3 
47"-45 

46-55 

+0-90 

Weighted  mean             =  34    08 

47    -45 

drO'-'-I2. 

e  =  ±  o"-6c 

). 

133  observations,  26  pairs. 

[Reduction  to  A  =  +  o"-26.] 

i 


THE    ASTRONOMIC    MEASURES. 


305 


62.  ,  \tlauta  Middle  lUisi 
1.S72.  One  division  of  k-vfl  = 
tions  at  this  station. 


,  (ieorj^ia.    -1'.  I'.  Webber.     Zenith  telescope  No.  5.     September  4  lo  27, 
\"  (X).     One  turn  of  micrometer  =  41"  427  from  circumpolar  ob.serva- 


I'airs 

of  stars. 

Adopted  seconds  of 
mean  N.  V.  D. 

«' 

w 

Latitude. 

V 

/t 

// 

0      /       // 

// 

6  109 

6   134 

2976 

28  -(XJ 

5 

7 

33  54  21  -68 

+014 

6  452 

6  4.S7 

2216 

1 4  -(X) 

5 

7 

20  -98 

4-0-84 

6  5H3 

6  595 

29    28 

fxj  -70 

5 

7 

21  -48 

-^0-34 

6  656 

6  676 

36    16 

38-4' 

5 

7 

21  -80 

-J-0  02 

6  697 

6  724 

3 1  'So 

22  20 

5 

7 

22  -15 

-0-33 

6  739 

6  763 

42   25 

15  73 

5 

7 

22  03 

—  0-2I 

6  777 

6  800 

53  -So 

5470 

5 

7 

20  -64 

-(-I  -18 

6  S39 

6  S81 

08  -50 

41  '09 

5 

7 

20  -96 

+  0-86 

6  92.S 

6  952 

44 '30 

25-72 

6 

7 

2'   53 

^  029 

6  97S 

7  "27 

00  ■  1 0 

55  '03 

5 

7 

22  -91 

—  I  -09 

7  061 

7  "67 

4470 

26-26 

5 

7 

21  -63 

-0-19 

7   164 

7  213 

4,S  -05 

43 -'5 

5 

7 

21  -99 

-0-17 

7  336 

7  368 

43  '24 

49 '3 1 

5 

7 

21  -60 

-t-O-22 

7  431 

7  450 

32  -92 

40  -lo 

5 

7 

21   62 

4-0  -20 

7  520 

7  548 

21  -88 

50 '34 

5 

7 

21  -41 

-1-0 -41 

7  602 

7  607 

13-42 

14-82 

_  5 

7 

22-47 

-0-65 

7  631 

7  664 

15 -78 

31  -'5 

5 

7 

21  69 

+  0-13 

7  695 

7  712 

'675 

09-92 

5 

7 

20-63 

+  1  -19 

7  754 

7  796 

47  -44 

19  -82 

5 

7 

21  -74 

+0-08 

7  880 

7  914 

39-28 

35  '30 

5 

7 

21  -75 

4-0-07 

7  94S 

7  958 

4'  79 

25  'oiJ 

5 

7 

21  -86 

—  0  -04 

S  032 

8  037 

39-'i 

55-81 

5 

7 

20  ■  60 

+  1  -22 

S  054 

8  071 

iS  -20 

1 6  60 

5 

7 

21  -52 

-0-30 

8  115 

8  131 

33  -68 

36-09 

5 

7 

22  -19 

-0-37 

8  203 

8  224 

25  61 

06  67 

5 

7 

22  -24 

-0   42 

8  250 

8  26S 

44-62 

39  20 

5 

7 

21  -67 

+  0-15 

8  330 

s  370 

26-62 

57  '53 

5 

7 

22  -46 

0-64 

63 

S3 

36  -22 

45-87 

5 

7 

20  -84 

-0-98 

120 

158 

30-40 

18-53 

5 

7 

22-44 

—  0   62 

168 

'97 

25    29 

16  -07 

5 

7 

21  -51 

+  0-31 

6  475 

6  542 

18-47 

44-58 

5 

7 

21  -69 

-0-13 

6  678 

6  721 

57 'oS 

47  -84 

5 

7 

22-41 

-059 

6  745 

6  758 

33  '62 

58  -97 

5 

7 

22  22 

—  0-40 

6  7S0 

6  805 

l6-12 

11  -64 

5 

7 

21  69 

+o-:3 

6  865 

6  868 

27-14 

54  -36 

5 

7 

21  -31 

-0-51 

6  962 

6  975 

14-50 

32  '3" 

5 

7 

22  07 

-025 

7  "41 

7   "7 

46  -98 

37   15 

6 

7 

21  00 

+  0  82 

7   "46 

7   '53 

35  '47 

23  -88 

5 

7 

22  44 

—0-62 

7   166 

7  223 

42  -98 

55  -00 

5 

7 

22  03 

—  0  -21 

7  256 

7  260 

40  -85 

00  -03 

5 

7 

21  -54 

-TO   28 

7  350 

7  417 

57  -93 

02  dx 

5 

7 

21  -71 

-t-OII 

7  4,S3 

7  465 

"4  '57 

01  -52 

5 

7 

22  -77 

—  0  -Q.S 

4192— 

No.  7 — 02- 

20 

io6 


THE    EASTERN    OBLIQUE    ARC. 

Atlanta  IMiddle  Base,  Georijia — continued. 


Pairs  o 

f  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

„' 

■"■' 

Latitude 

z/ 

// 

// 

0      /        // 

// 

7  544 

7 

571 

23  '41 

32  -50 

5 

7 

33   54   21 

-55 

4-0  -27 

7  668 

7 

674 

13-61 

55-06 

6 

7 

21 

-96 

—0  -14 

7  727 

7 

733 

31  '64 

00-75 

5 

7 

22 

-27 

-0  -45 

7  901 

7 

923 

55  06 

50-55 

5 

7 

22 

-36 

-0  -54 

7  937 

7 

995 

25  '96 

57  ■S8 

5 

7 

22 

•87 

- '  -05 

8  052 

s 

076 

19  "57 

34  -05 

5 

7 

22 

-33 

"O-51 

8  125 

8 

147 

36  '34 

32-05 

5 

7 

21 

-55 

+0-27 

8  212 

S 

284 

08  -20 

II  -50 

5 

7 

22 

-37 

-  0  -55 

8  300 

8 

364 

53-12 

50-24 

6 

7 

21 

-13 

-|  0  -69 

54 

lOI 

40  -84 

57  -45 

5 

7 

22 

-45 

—0  -63 

152 

178 

04  -34 

22-39 

5 

7 

22 

•32 

—0  -50 

198 

217 

59  -42 
Indi.scriniina 

28-50 
te  mean 

^ 

5 

1  -lO    1-1' 

oj    54 

/ 

2l''-82 

22 

•09 

-0-27 

■Weighted  mean 

= 

33    54 

2  r    -82 

±o''-05 

c 

= 

±o''-3 

5 

274  observations,  54  pairs. 

[Red 

notion  to 

A 

=  ^-o" 

-40.] 

63.  Atlanta,  Georgia. — C.  H.  .Sinclair.  Meridian  telescope  No.  13.  January  i  to  22,  1880.  One 
division  of  level  =  2"  "]  at  33°  F.  and  2"  -64  at  75° -2  F.  One  turn  of  micrometer  =  77"  -783  from 
circuripolar  observations  at  this  .station. 


Pairs  of  stars. 


522 
628 
682 
S19 
897 

974 
I  006 
I  065 

(557) 
I  139 
I  214 
I  254 
I  301 
I  307 
I  382 
I  409 
I  460 

(772) 
I  500 


Adopted  seconds  of 
mean  N.  P.  D. 


08  -80 

44-71 
28  -85 
50-72 
26  -10 

43  -72 
08  -58 

32-79 

52  -20 
03-10 
58-22 

55  -50 
25-50 

53  -25 
17-50 

55-20 

29-50 

04  -80 

32-12 
Indiscriminate  mean  =  33°  44'  59''  -34. 
Weighted  mean  =33     44    59      30 

('  =  zb  o"  -50. 

93  observations,  19  pairs. 

[Reduction  to  A  =  +  o"  -08.] 


592 

00  'OO 

657 

49-20 

706 

13  -04 

842 

12-40 

921 

25  -63 

981 

56  -90 

I  052 

02  -67 

I  087 

55  -So 

I  129 

37-76 

I  192 

07  -20 

(654) 

14  -60 

I  272 

34  -60 

I  346 

05  -68 

I  365 

42-75 

I  393 

oS  -00 

I  424 

33  -So 

X  456 

43  -50 

I  492 

22  -02 

I  504 

03-40 

Latitude. 
o       /  // 

33  44  58  -83 
58-42 

59  -3^ 
59-25 
5S  -63 

60  -44 

59-5S 
58-99 
59-12 
59  -48 
58-19 
60-51 

58-30 
60-26 
58-92 
59-45 
59-66 

61  -14 
58-85 

d=  0-I2. 


+0-47 

+0-8S 
— o'oS 
+0-05 
+0-67 
-I  -14 
— o  -28 

+0-31 
+0-18 

-o-i8 
+  I-II 

—  I  -21 

+  1  -OO 

— o  -96 

+0-38 
-0-15 
—0-36 

-1-84 
+0-45 


THK    ASTRONOMIC    MEASTRES. 


307 


64.  A'a/ialiiur,  Alahaiiia. — ().  ]'..  I'Vciich.  /eiiilh  Iclescojjc- Xo.  2.  June  3109,  1898.  One  division 
of  level  =  i""2i  I,  as  determined  by  K.  (>.  I'ischer,  1.S91.  One  turn  of  micrometer  =  46"'376  from 
latitude  ohserNations  at  this  station. 


I'aii's  ol  slar.s. 


1| 


4  729 

*4  74S 

*4  748 

4  762 

*(2    232) 
*(2    237) 

4  830 
4  873 
4  936 

4  967 
(2  350) 
*5  098 
*5  098 

5  143 
5  iSi 
5  287 

(2  4S6) 
5  3SS 
5  509 


4  741 
*(2  232) 
'"(2  237) 

*(2    237) 

*4  792 
*4  792 
4  847 1- 
4  9071' 

4  939 
(2  339) 
(2  358) 
(2  396) 
■(2  399) 

5  155 
5  216 

*5  322 

*5  322 

5  462 

5  523 


A(l<)]He(l  seconds  of 
mean  N.  P.  U. 

11' 

w 

LatiUulc. 

V 

// 

// 

0      /         // 

// 

1 1  "45 

36-36 

4 

>3 

33   13  39 '87 

+0-03 

38  -32 

04-04 

2 

5 

39-49 

+0-41 

38-32 

56  -63 

4 

7 

39  45 

+045 

18-51 

56-63 

2 

5 

38-99 

+0-91 

04  -04 

14-73 

2 

5 

40-45 

-055 

56  -63 

14-73 

4 

7 

40  -07 

-0-17 

12-97 

40  -08 

4 

13 

39-95 

—0-05 

13  70 

36  -85 

5 

14 

39  -80 

+0-10 

39-62 

5'  -24 

5 

14 

3972 

^o-i8 

41  -07 

32-25 

5 

14 

40  -29 

-039 

47-42 

21  -87 

4 

12 

40-54 

—0-64 

33-99 

53-58 

4 

9 

39 -58 

4-0  32 

33-99 

09  15 

3 

S 

39  -78 

--0-12 

3' -89 

04-40 

4 

'3 

39 '40 

—0-50 

38  -78 

32-52 

4 

13 

40-43 

-0-55 

51  -95 

44-83 

4 

9 

40-30 

—0-40 

44-46 

44-83 

3 

3 

39-60 

+0-30 

59  "76 

56-50 

4 

'3 

39  -60 

-0-30 

17 '33 

38-06 

4 

>3 

39  "92 

-0  -02 

criminate 

mean  = 

■,-,0 

13'  39" 

■85- 

tited  mean           = 

33 

13    39 

-90- 

o''-o6. 

c  — 

±0 

"■31- 

71  observations,  19  pairs. 

[Reduction  to  A  =i-o"-39.] 

65.  Montgomery,  Alabama. — G.  W.  Dean.  Zenith  telescope  No.  5.  March  22  to 
division  of  level  =  a"  "929  as  determined  at  this  station.  One  turn  of  micrometer 
circumpolar  observations  at  this  station. 

Adopted  seconds  of 
mean  N.  P.  D. 


28,  1S56.     One 
=  41" -45  from 


Pairs  of 

stars. 

3   '09 

3     '12 

3   '40 

3  '76 

3  202 

3  220 

3  241 

3  255 

3  307 

3  327 

3  33' 

3  352 

3  399 

3  423 

3  5 '5 

3  522 

*3  545 

3  548 

*3  545 

3  560 

3  580 

3  621 

*3  634 

3  665 

11  -iS 

07   13 

14  -oS 

17-90 

16  72 

42-66 

46  -01 

48-07 

18-20 

55  ■  1 1 

54  'o>i^ 

00  -86 

39-20 

29-80 

16  -10 

00-00 

26  -90 

16-96 

26  -90 

19-90 

57  -So 

23-07 

27  -20 

27  00 

11' 

7V 

Latitude. 

:• 

0      /           // 

/' 

5 

14 

32  22  45  -66 

-0   25 

5 

14 

45-68 

-0-27 

5 

14 

45   19 

+  0-22 

4 

13 

45«4 

•0-27 

4 

13 

44-34 

•i-i  07 

4 

'3 

45-42 

— o-oi 

4 

13 

45  95 

-  0  54 

6 

14 

45  93 

-  0  52 

6 

lO 

45-09 

-  0  -32 

6 

10 

44-89 

-  0  52 

6 

14 

45  "35 

-rO-06 

5 

9 

44 -So 

-  0  -61 

I 


3o8 


THE    EASTERN    OBLIQUE    ARC. 

65.   Mo'iti^oincry,  Alabama — continued. 


Pairs  of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

w 

7C 

Latitude. 

V 

// 

// 

0       /          // 

// 

*3  634 

3 

670 

27  -20 

'  5  -40 

5 

9 

32    22    44-96 

+0-45 

3  704 

3 

736 

23  '04 

50  -53 

6 

14 

45  -86 

-0-45 

3  760 

3 

776 

44 '44 

55  -07 

5 

14 

45  -38 

+0-03 

3  S25 

3 

837 

26-18 

07-13 

5 

■4 

45  -81 

—0  -40 

3  885 

3 

911 

38  '35 

24-17 

5 

14 

45  -15 

+0  -26 

3  931 

3 

954 

09  -98 

08  -27 

5 

14 

45  -75 

-0  -34 

3  964 

3 

973 

52  -30 

42-17 

5 

14 

45  -41 

0  -oo 

*3  990 

4 

057 

51  -22 

19-75 

5 

9 

45-14 

+0-27 

*3  990 

4  059 

51  '22 

37  -41 

5 

9 

45  -60 

— 0  -19 

4  079 

4 

121 

05  -62 

49-60 

5 

'4 

45-64 

-0-23 

4   127 

*4 

1 88 

13-94 

55  -48 

4 

9 

45  -66 

--0-25 

4   184 

*4 

188 

2576 

55  -48 

5 

9 

45  -56 

-0-15 

4  203 

4 

229 

22  -14 

39  -46 

5 

14 

44-72 

+0  -69 

4  240 

4 

258 

37-09 

56  "60 

4 

13 

45  -67 

—  0  -26 

4  2S7 

4 

351 

1 8  -35 

47  -80 

5 

14 

45  -40 

-f  0  -01 

4  384 

4 

390 

46  -34 

04  -56 

5 

14 

45  -67 

—0-26 

4  421 

4 

457 

26  -53 

52  -70 

5 

'4 

44-95 

+0-46 

4  468 

4 

538 

38-73 

47  -78 

5 

H 

44  -80 

-t-o  -6r 

4  553 

*4 

596 

03  -'6 

14-57 

5 

9 

45-69 

-0  -28 

4  566 

'■'4 

596 

23  -37 

'4-57 

5 

9 

45  -10 

+0-31 

4  609 

4 

618 

52  -22 

10-25 

5 

14 

45-26 

^0-15 

4  632 

4 

640 

28-1,3 

29-75 

5 

14 

45  -66 

-0-25 

4  694 

4 

714 

35-61 

32  -09 

2 

9 

45  -66 

-0-25 

4  699 

4 

729 

32-67 

57-47 

2 

9 

46  -01 

—0  -60 

4  753 

4 

827 

53-46 

50-70 

2 

9 

45-94 

-0  -53 

4  789 

4 

853 

55  -76 

58-71 

2 

9 

46-03 

—0  -62 

4  902 

4 

96  r 

08-17 

41  -02 

2 

9 

45-50 

— 0  "og 

4  993 

5 

026 

17  -16 

38-94 

2 

9 

45-80 

-0.39 

Indiscriminate  mean  =  32°  22'  45''  -43. 
"Weighted  mean     •      =32     22    45     -4i=bo"-o4. 

e  =  ±  o"  -29. 
181  observations,  40  pairs. 
[Reduction  to  [^  or  center  of  State  House  =  -j-  o"  -22.] 


THK    ASTRONOMIC    MEASURES. 


309 


66.    /. owe r  Peach    7>rd',  Alabama.   -\i.  (ioodfellov^ ,     Zenith   li- 
One  division  of  level  =0''' '99  from  ob.servation.s  at  this  station, 
from  circiimpolar  ob.servationH  at  Mobile,  Alabama. 


U-seope  No.  5.     April  4  to  16,  1S57. 
One  turn  of  micrometer  =  41''' '481 


P.'tirs  (if  stars. 


2  740 
2  841 
2    912 

2  995 

3  047 
3  095 
3  140 
3  246 
3  278 
3  355 
3  406 
3  505 
3  545 
3  610 
3  661 
3  691 
3  725 
3  862 
3  915 
3  981 

*4  017 
*4  017 


2  792 

2  S60 

2  952 

'3  "75 

''"3  "75 

3  lo^ 
3  228 
3  265 
3  34' 
3  399 
3  421 
3  522 
3  602 
3  650 
3  685 
3  729 
3  788 
3  885 
3  952 

3  995 

4  027 
4  072 


Acloi)te<l  seconds  of 
iiieaii  N.  P.  O. 


4 

4 
4 
4 
4 
3 
5 
4 
5 
4 
4 
4 
4 
4 
4 
4 
'5 
4 
6 

5 
6 

4 

Indiscriminate  mean  =31°  50'  2i""iS. 
Weighted  mean  =31    50    21    '19: 

r  =  ±o"-53. 
95  observations,  22  pairs. 

[Reduction  to  ^^  =o"oo.] 


29  "3 

27  -05 

<J2  -68 

56-19 

21  76 

15  -52 

iS  '92 

52  -87 

54  -29 

52  -87 

01  Mfi 

17-82 

28  -60 

24-15 

14  '(X) 

47  -5" 

25-27 

54-68 

23  '50 

56  -05 

29  -83 

10  -38 

24  -07 

18  -09 

45 -0(3 

16  -58 

34-50 

50  -40 

21  -90 

56  -73 

20-64 

59-19 

21  -84 

30-80 

15  -50 

58  -02 

II  -30 

55-06 

40  "12 

43  -39 

37 -'5 

39  -20 

37-15 

21  -00 

w 

I<atiturle 

V 

0      /          // 

// 

5 

31    50   21-03 

+0-16 

5 

21  -68 

-049 

5 

20  -75 

-fo-44 

3 

21  79 

— o-6o 

3 

21  04 

-f-0-15 

4 

22-37 

-1  -18 

5 

21    16 

4-0  03 

5 

20  22 

+0-97 

5 

20  -61 

+0-58 

5 

21   95 

—0-76 

5 

21  -37 

—0-18 

5 

20-74 

-t-0-45 

5 

22  '41 

—  I  -22 

5 

21  40 

—  0  -21 

5 

20  -61 

40-58 

5 

21  37 

—0  -rS 

5 

20  -88 

4-0-31 

5 

22  -38 

-I  -19 

5 

20-64 

+0-55 

5 

20-71 

+0-48 

4 

20  76 

+0-43 

3 

20-16 

+  1  -03 

3IO 


THE    EASTERN    OBLIQUE    ARC. 


67.  Coon,  Alabama. — O.  B.  French.  Zenith  telescope  No.  2.  May  21  to  26,  1S98.  One  division 
of  level=i"'2ii  as  deterniined  April  23,  1.S91.  One  turn  of  micrometer=46''-325  from  circumpolar 
observations  at  this  station  and  at  Kahatchee,  Alabama. 


Pairs  of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

«' 

w 

Latitude. 

V 

// 

// 

0      / 

// 

// 

4    122 

4  140 

56  -lo 

51-58 

4 

20 

34   14 

48  -26 

-0-44 

4    222 

4  257 

01  -51 

03-45 

5 

24 

47-77 

-t  0  -05 

4    268p 

4  300 

21  -iS 

44-39 

5 

15 

47  -86 

—0  -04 

4  347 

4  352 

29-62 

42-79 

5 

24 

47-78 

+0-04 

4  3S7 

4  433 

58  -04 

25-56 

4 

21 

47  -93 

—0  -ri 

4  4S0 

4  506 

44-10 

44  -33 

4 

21 

48  -00 

— o-iS 

4  513 

4  536 

12  -91 

42  -60 

2 

10 

47-11 

+0-71 

(2  122) 

4  591 

19  -62 

54-04 

4 

21 

47  -88 

—0  -06 

4  607 

(2   15S) 

39  79 

50-40 

5 

21 

47-91 

—0  -09 

*4  727 

(2  232) 

49-88 

04-04 

4 

14 

48  -06 

—0  -24 

*4  727 

(2  237) 

49  -88 

56-63 

4 

14 

48-19 

-0-37 

4  S03 

4  8?3 

17-95 

42  -80 

5 

15 

47  -88 

—0  -06 

4  843 

4  873 

19-29 

13-70 

5 

24 

47-46 

+0-36 

(2  288) 

4  706 

35 '02 

34-43 

5 

19 

47-29 

+0  -53 

I 
6 

ndiscriminate  mean  =  31°   14' 
Weighted  mean          =31      14 

■   ,'=±o"-34 
I  observations,  14  pairs. 

[Reduction  to  A  =  — 

47''-Si. 
47    ■S2ihO 

3"-o3.] 

"•05. 

68.  Rlokilc,  Alabama.— E.  Goodfellow.  Zenith  telescope  No.  5.  December  11,  1856  to  January  3, 
1857.  One  division  of  level  =  0^-69.  One  turn  of  micrometer  =  4i"-4Si  from  circumpolar  observations 
at  this  station. 


Pairs 

of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

«' 

W 

Latitude. 

V 

// 

// 

0       / 

// 

// 

215 

259 

01  -20 

57-08 

5 

6 

30  41 

33  -86 

-0-44 

283 

307 

47-90 

56-18 

6 

6 

32-68 

+0-74 

330 

341 

37-96 

36-70 

6 

6 

32-32 

+  1  -lO 

*425 

427 

27  -05 

44-09 

6 

4 

32-55 

+0-87 

*425 

431 

27  -05 

26-03 

7 

4 

33-11 

+0-31 

446 

^492 

24-74 

53  -32 

6 

4 

33  -28 

+0-I4 

469 

'492 

34-76 

53-32 

6 

4 

32-97 

+0-45 

510 

523 

40  -06 

59-27 

6 

6 

33-00 

+0-42 

556 

566 

30-03 

58-50 

6 

6 

33-00 

+0-42 

576 

630 

5'  -79 

38-00 

6 

6 

31  -99 

+  1  "43 

648 

661 

14-22 

32-61 

6 

6 

33-88 

—0  -46 

THE    ASTRONOMIC    MEASURES. 


3" 


68.  Mobile,  Alabama — continued. 

Pairs  of  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

«' 

w 

latitude. 

V 

// 

// 

0      /        // 

// 

697 

•^710 

13  -48 

26  -80 

6 

4 

30  41  33  -58 

—0  16 

69S 

*7io 

'5  75 

26  80 

6 

4 

34-13 

-0-71 

735 

798 

33  78 

44  -90 

6 

6 

32-86 

+0-56 

872 

9'5 

09  -44 

50  -42 

6 

6 

33  -27 

-015 

921 

963 

18-03 

09  -06 

6 

6 

34  -02 

—0  -60 

9.S6 

993 

15-97 

=  5-73 

6 

6 

33  -85 

-0-43 

I  006 

064 

28  -69 

01  -30 

6 

6 

33-33 

-^0  09 

I  095 

-X-j 

123 

20  70 

18-58 

7 

3 

33  -69 

—0  -27 

-I   123 

146 

18-58 

01  -62 

6 

3 

34-24 

-0-S2 

-I   123 

154 

18  -58 

09  -0() 

7 

3 

34-23 

-o-8i 

I   189 

Xj 

219 

50  -57 

37-60 

6 

3 

33-68 

—0  -26 

I   219 

257 

37  '60 

55-27 

6 

3 

33  -77 

-0-35 

"1   219 

260 

37  '60 

(« -23 

6 

3 

34-47 

-I  -05 

I  323 

328 

59  92 

26-34 

7 

6 

33-32 

^0  10 

I  337 

*T 

414 

22  -60 

08  -84 

5 

4 

32  -68 

^074 

I  342 

*I 

414 

22  -80 

08  -84 

7 

4 

33  -6<-> 

-o-i8 

1  445 

468 

50-53 

47-40 

6 

6 

33  "52 

—0  -lo 

I  492 

528 

41  -55 

34-60 

6 

6 

34  -50 

-:-o8 

I  557 

*] 

609 

02  -42 

13-00 

7 

4 

32  -83 

+0-59 

I  59f 

*I 

609 

27  -12 

13  -oo 

5 

4 

32-43 

+099 

I  629 

*I 

64S 

33-21 

36  -54 

6 

4 

33-67 

-0-25 

I  632 

*I 

64S 

34  -83 

36-54 

6 

4 

32-91 

-ro-51 

I  669 

768 

45-50 

52 -88 

6 

6 

33-15 

-0-27 

I  845 

925 

56-45 

28  -05 

6 

6 

33-32 

+  0-I0 

I  935 

951 

05  -36 

10  -19 

6 

4 

33  20 

-^0-22 

I  935 

2 

016 

05-36 

54-31 

6 

4 

33  -48 

—0-06 

2  067 

2 

155 

47-13 

13  -70 

6 

6 

34-29 

-0-87 

2  182 

2 

228 

33-06 

16  -11 

5 

6 

33-57 

-015 

2  306 

2 

409 

28  -40 

10-93 

6 

6 

34  -37 

-0-95 

2  423 

2 

429 

19-10 

18-03 

4 

5 

33  -37 

+005 

2  441 

2 

444 

28-79 

oS  -55 

6 

6 

33-17 

-^025 

2  463 

2 

563 

34-28 

05-83 

6 

6 

34-38 

—0-96 

111 

liscriiiiiiiate  mean  =30°  41'  33" 

43- 

W 

;ij!;hled  mean 

=  30 

41    33 

-42  ±o"-o6. 

<'=  ± 

o"-  46. 

25' 

^  observations 

43  P<»*-s- 

[Rt 

iduction  to  A  (Episcopa 

1  Church. 

')=  - 

io"-72.] 

312 


THE    EASTERN    OBLIQUE    ARC. 


69.  iT(75/ /'(75r(roo«/(r,  Mississippi. -R.  H.  Fauntleroy.  Zenith  Telescope  No.  r.  June  25  to  July 
26,  1847.  One  division  of  level  =  o"  '90.  One  turn  of  micrometer  =  45"  '502  from  latitude  observa- 
tions at  this  station. 


Pairs  0 

f  stars. 

Adopted 
mean 

seconds  of 
N.  P.  D. 

n' 

w 

Latitude. 

7' 

// 

// 

0       /         // 

// 

5  463 

5  563 

ID  -60 

57-00 

2 

12 

30   20  41  -19 

-0-27 

5  628 

5  724 

I  2  -36 

17-13 

I 

6 

40  -87 

+0-05 

5  667 

5  749 

50-65 

oi  -25 

3 

'9 

40-43 

+0-49 

5  795 

5  940 

39  77 

'9-77 

2 

12 

40-79 

+o-'i3 

5  S02 

5  853 

29  78 

31  -96 

2 

12 

40-91 

+0  -01 

5  953 

6  006 

12  '40 

19  -20 

3 

19 

40-57 

+0  -35 

6  013 

6  094 

44-92 

09  -65 

2 

12 

41  -08 

—0  -16 

6  052 

6   143 

49-24 

12  -lo 

I 

6 

40  -82 

+0  -10 

6  155 

6  2i5 

39  79 

44-99 

I 

6 

40-44 

+0-48 

*6  224 

6  4r8 

14-98 

57-12 

3 

12 

41  -71 

-0-79 

*6  224 

6  420 

14-98 

29-64 

3 

12 

40  -60 

+0-32 

6  269 

6  373 

23  -53 

48  -06 

4 

24 

4r  -51 

-0  -59 

6  42S 

%  615 

18-42 

13-29 

4 

12 

40-70 

■f  0  -22 

6  476 

%  615 

46  -40 

13-29 

3 

9 

40-62 

+0  -30 

6  460 

6  5-^3 

27-50 

59-08 

2 

8 

41  -26 

-0-34 

6  626 

*6  644 

42-71 

42-24 

3 

12 

•     40  -76 

+o-i6 

*6  644 

6  717 

42  -24 

07  -50 

3 

12 

40  '80 

+0  -12 

6  720 

6  744 

17  -06 

27  -39 

.    3 

'9 

40  -98 

—0  -06 

6  748 

6  833 

58  -80 

17  -10 

3 

'9 

40-32 

1  0  -60 

6  772 

-6  865 

20-15 

23-86 

3 

12 

40-67 

f  0-25 

6  805 

^^•6  865 

48  -38 

23-86 

3 

12 

41  -lo 

— o-i8 

6  891 

6  932 

53  -88 

5'  -27 

4 

24 

40  -85 

+0-07 

6  910 

6  970 

51  -61 

01  -18 

3 

19 

40  -18 

^-0-74 

6  985 

7  088 

I'  75 

47  -30 

4 

24 

40-52    ■ 

+  0-40 

7  062 

7  223 

18-98 

24-77 

3 

'9 

40  -68 

+0-24 

7  091 

7  257 

37-60 

47-3' 

3 

'9 

40  -78 

+0-14 

7   125 

7   182 

09  -ro 

26  -39 

5 

29 

41  -22 

—0  -30 

7  215 

7  269 

04-05 

25-4' 

5 

29 

40-51 

+0-41 

7  324 

7  401 

35-18 

34-71 

2 

12 

41   •21 

—0-29 

7  350 

7  448 

53  "53 

56-16 

3 

'9 

41   -16 

-0  -24 

7  476 

7  527 

50  -78 

29-07 

4 

24 

41   ■\\ 

—0  -22 

7  488 

*7  561 

47-00 

25  -73 

3 

12 

40-63 

+  0  -29 

7  589 

"7  561 

08  -90 

25  -73 

3 

12 

40-24 

+  0-68 

7  642 

7  662 

28  -69 

31  69 

3 

19 

40  -69 

+0-23 

7  606 

7  705 

22  -40 

41  -54 

2 

12 

41  79 

—  0  -87 

*7  689 

7  754 

12-97 

12-49 

3 

12 

41  -42 

0-50 

*7  689 

7  77« 

12-97 

04-36 

3 

12 

41  -42 

0-50 

*7  766 

7  795 

51  -04 

22  -52 

2 

8 

41  -oo 

-  0  -08 

*7  766 

7  809 

51  -04 

42-31 

I 

4 

41  -72 

-0  -80 

7  812 

7  827 

16-86 

10-45 

3 

19 

41  -24 

-0-32 

I 


Pairs  of 

stars. 

7  -'^45 

7  9'2 

7  888 

7  908 

7  953 

7  99^ 

7  975 

8    115 

8  036 

8    149 

«   "53 

8  218 

8  262 

8  282 

8  322 

8  33' 

THE    ASTRONOMIC    MEASURES, 


69,    luxst  /'asrni^oiiUi ,  Mississippi — rfuilimu-d. 

Adopted  seconds  of 
mean  N    I'.  I). 


3^3 


29  '35 

51  70 

36  -03 

56-60 

23 -.6 

27  29 

43  ■ '  2 

25  -60 

09  ■  y  f 

43  -83 

17-58 

46  -45 

42  75 

1 1  -98 

42  -55 

01  -65 

11' 

w 

Latitude. 

V 

0 

/          // 

// 

I 

6 

S"-' 

20  41-39 

-0  -47 

4 

24 

40  96 

-0  -04 

4 

24 

4'  '^7 

-075 

I 

6 

40  -68 

i  0-24 

3 

19 

41  -04 

-f)  -12 

I 

6 

40-35 

^0  -57 

2 

12 

40  -59 

+0  -33 

2 

12 

40  93 

—0  -01 

I 


Iiidiscriiniiiale  iiiciin  =  30°   20'  40" '92. 
Weifjhtt'd  iiit-an  =  30     20    40    -92  +:  o"  -04 

I?  =  rtr  o"  -39. 

129  oh.servations,  48  pairs. 

[Reduction  to  A  =  o"  'no.] 

70.  Fori  Morgan,  Alabama. — R.  H.  Fauntlero)-.  Zenith  telescope  No.  i.  March 
1847.  One  division  of  level  =  o"  -91  from  observations  at  this  station.  One  tnrn 
=  45"  -570  from  latitude  observations  at  this  station. 


23  to  April  30, 
of  micrometer 


fairs  t 

f  stars. 

Adopted  seconds  of 
mean  N.  P.  D. 

«' 

?<■ 

Latitude. 

V 

// 

// 

0      /         // 

// 

2   650 

2 

673 

34  -45 

58-17 

4 

24 

30    13   47-92 

-0-03 

2   725 

2 

765 

32  42 

38 -CXI 

4 

24 

48-22 

-0-33 

2    844 

2 

889 

22  -03 

oa  -70 

4 

24 

47-91 

— 0  -02 

2    970 

3 

<75 

57  ■<>3 

33  -87 

4 

24 

48-08 

—0-19 

3  105 

3 

140 

59  -36 

03-52 

7 

42 

47-75 

+0-14 

3   -82 

3 

25' 

31  '55 

45-44 

8 

48 

47  -78 

-f  o-ii 

3  325 

3 

368 

42  -30 

44-12 

10 

59 

47-96 

—0-07 

3  402 

3 

532 

33  ■40 

33  -90 

'3 

77 

47-67 

+0-22 

3  592 

3 

682 

'9  97 

44  -80 

15 

9" 

48  -20 

-0-31 

3  758 

3 

843 

■7  75 

32  -04 

16 

100 

47  -52 

+0-37 

3  868 

.1 

910 

42  -68 

32-3' 

13 

77 

48-13 

-0-24 

3  949 

3 

979 

02  -56 

29  -34 

14 

83 

48  -oS 

—0-19 

4  094 

4 

123 

33  95 

w  95 

1 1 

67 

47-66 

+0-23 

4  228 

*4 

303 

34  -28 

52  92 

10 

59 

47-92 

—0  -03 

4  271 

•'^4 

303 

12-79 

52-92 

10 

59 

48-10 

— 0-2I 

4  341 

4 

423 

20-69 

42  -65 

8 

48 

47  -73 

+  0-16 

4  596 

4 

637 

31  -28 

38  -80 

7 

42 

47  -84 

+  0  -05 

4  699 

4 

737 

56  67 

33  -72 

5 

30 

47-67 

-1-0-22 

4  792 

4 

874 

20  -54 

04  -89 

^> 

18 

47  -91 

-0  -02 

Ii 

idiscriininate 

mean  = 

30^ 

13'  47 

"  -9<-). 

\ 

l^eighted  mean           = 

30 

'3   47 

•894, 

0"  -03. 

f  = 

rt  0 

"-4.. 

If 

16  observations,   19  pal 

rs. 

[Re. 

Inction  to  A 

=  0" 

CKl.  1 

314 


THE    EASTERN    OBLIQUE    ARC. 


71.  AVttv  OrA'rt;/.?,  Louisiana.— J.  Kincheloe.  Zenith  telescope  No.  5.  January  r6 
185S.  One  division  of  level  =o'''845  from  observations  at  this  station.  One  turn 
=  4i'''5i6  from  circumpolar  observations  at  this  station. 

n'  w  Latitude. 


to  February  10, 
of  micrometer 


Pairs  of  stars. 

707 

727 

745 

749 

766 

772 

806 

*905 

885 

-905 

-981 

999 

*98i 

I  034 

I  066 

I  084 

1    107 

I    123 

I  221 

I    269 

'i  323 

J   335 

'I  323 

I  343 

I   376 

I  414 

I   449 

I  476 

I   492 

I  527 

I  571 

I  602 

I  631 

I  651 

I  69C3 

I  778 

I  834 

•■■■I  897 

I  862 

*i  897 

I  935 

I   970 

'I  981 

2  014 

-I  981 

2  021 

2  084 

*2     155 

2  090 

*2     155 

2  200 

2    228 

2  237 

2    254 

2  30' 

2    340 

-2  440 

2    464 

'2  440 

2    485 

-2  504 

2  5'4 

-2  504 

2    551 

2  639 

2    691 

2  73' 

2  79« 

2  892 

2  97' 

3  000 

■■■3  016 

3  002 

■■3  016 

3  035 

3  075 

3   >23 

3   162 

3   '«2 

3  227 

.'Adopted  seconds  of 
mean  N.  P.  D. 

// 

// 

28  -20 

01  -40 

05  -00 

04-29 

47-04 

06  -90 

39  '33 

32  -23 

19 '58 

32  -23 

51  -91 

04  -94 

51  '9' 

04 -3  > 

1274 

13  -68 

43 '34 

54-32 

04  -42 

09-78 

41  '66 

43  -73 

41  '66 

44-52 

17-23 

52  -9S 

09  '60 

59-92 

28  -29 

37  -70 

13  '98 

IS -08 

54  '99 

03  -30 

59 '50 

1 2  -50 

21  76 

52  -84 

04  -98 

52.  84 

04  -66 

28  -33 

]  I  '46 

28-15 

II  '46 

2,S  -61 

20-45 

18  -90 

07  -88 

1 8  -90 

ID  -lO 

23  -24 

19  -61 

03  -50 

43  '35 

34  -80 

30-55 

13  -88 

30-55 

16-34 

'5  -25 

33  -86 

15-25 

55  -30 

01  -88 

10-23 

II  -66 

29  -84 

40  -62 

46-44 

39  -43 

09  -33 

46-66 

09  '33 

02  -40 

06  -70 

46-78 

56  -49 

16-62 

38  -06 

5 

29  57  25-17 

+0'II 

5 

24  -43 

+0-85 

5 

24  -73 

+  0-55 

4 

24  -61 

+0.67 

4 

24  -66 

+0-62 

4 

26  01 

-0-73 

4 

25-30 

— 0  '02 

5 

24-90 

+  0-38 

5 

25-29 

—  0  -Ql 

5 

25  -39 

—  0  -11 

4 

26  -35 

—  I   -07 

4 

25-30 

—  0  -02 

5 

25  -50 

—  0  -22 

5 

25  -70 

—0-42 

5 

24  -06 

+  1.  22 

5 

25-83 

-0  -55 

5 

24  -88 

-I-0-40 

5 

24-16 

+  1  -12 

4 

25  -88 

—  0  "60 

3 

24-89 

+  0-39 

5 

24-43 

+  0  -85 

4 

26-05 

-0-77 

3 

26-45 

-I  -17 

4 

25  -60 

-0-32 

4 

26  -17 

-0-89 

5 

24-72 

+0-56 

5 

25  -72 

-0-44 

5 

25-51 

-0-23 

4 

25  -66 

-0-38 

4 

24  -43 

+0  -85 

4 

25  -23 

4-0-05 

4 

24-42 

+0  -86 

5 

26  -oi 

-  0-73 

5 

26  •r4 

-0-86 

5 

25  -25 

+0  -03 

4 

24-97 

+0-31 

4 

25-29 

-  0  -01 

5 

26-03 

-0  -75 

5 

25  -58 

—0  -30 

5 

24  -87 

i  0-41 

THE    ASTRONOMIC    MEASURES. 


315 


71.  New  Orleans,  Louisiana — continued. 


Pairs  of  stars. 


S  242 
.■^  ,V3 
3  35S 
3  3^1 


3  2S6 
3  327 
3  359 
3  39« 


'Adoptee 
mean 

seconds  of 
N.  P.  D. 

«' 

// 

// 

41  74 

4678 

6 

35  -86 

2975 

6 

29-64 

37  -80 

4 

43  '32 

44-40 

6 

w 

Latitude. 

V 

0      /          // 

// 

5 

29  57    26-12 

-0-84 

5 

24  -02 

+  1  -26 

5 

25  '35 

~o  o-j 

5 

25  -56 

-0-28 

Indiscriminate  mean       =  29°  57'  25'''-29. 
Weijfhted  mean  =29     57     25    -28^0" -07 

e  =  ±L  0^-43. 
256  ob.servations,  44  pairs. 

[Reduction  to  ^^  =  o^'-ckj.] 

3.  SUMMARY  OF  RESULTS  FOR  LATITUDE. 


No. 

Name  of  station. 

State. 

Resulting 
latitude. 

Probable  error 
of  result. 

0 

/ 

// 

// 

1 

Calais 

Me. 

45 

I  1 

09  40 

=!zO-o6 

2 

Cooper 

Me. 

44 

59 

12  -60 

005 

3 

Humpback 

Me. 

44 

5" 

47-56 

0-05 

4 

Bangor 

Me. 

44 

48 

1 2  -87 

005 

5 

Farmington 

Me. 

44 

4" 

19 '54 

005 

6 

Mount  Harris 

Me. 

44 

39 

54-66 

004 

7 

Howard 

Me. 

44 

37 

49 '24 

005 

8 

Mount  Desert 

Me. 

44 

21 

06-51 

003 

9 

Ragged  Mountain 

Me. 

44 

12 

42-96 

004 

10 

Sabattus 

Me. 

44 

oS 

37  73 

0  09 

II 

Mount  Pleasant 

Me. 

44 

01 

36-44 

0-04 

12 

Cape  Small 

Me. 

43 

46 

43  69 

0-04 

13 

Mount  Independence 

Me. 

43 

45 

34  -47 

006 

14 

Gun.stock 

N.  H. 

43 

31 

03  Si 

0-05 

15 

Agamenticus 

Me. 

43 

13 

24  96 

006 

16 

Isles  of  Shoals 

Me. 

42 

59 

12-97 

009 

17 

Unkonoonuc 

N.  H. 

42 

58 

59-34 

0  ^o^ 

18 

Thompson 

INIass. 

42 

36 

38  "02 

010 

19 

Wachusett 

INIass. 

42 

29 

16-13 

0  -04 

20 

Cambridge,  Harvard  College  Observatory 

Mass. 

42 

22 

48-05 

022 

21 

Cambridge,  Cloverden  Observatory 

Mass. 

42 

22 

40  -97 

0-08 

22 

Mount  Tom 

Ma.ss. 

42 

14 

27    62 

006 

23 

Manomet 

ISIass. 

41 

55 

35  '35 

005 

24 

Sandford 

Conn. 

41 

27 

40-47 

o-oS 

25 

West  Hills 

N.  Y. 

40 

48 

50  -06 

0-04 

26 

New  York 

X.  Y. 

40 

43 

48  -39 

009 

27 

Beacon  Hill 

N.J. 

40 

22 

27  -Si 

0-07 

28 

Mount  Ro.se 

N.J. 

40 

22 

05  -41 

0  oS 

29 

Yard 

Pa. 

39 

58 

29-39 

006 

*  Center  of  dome. 

3^6 


THE    EASTERN    OBLIOl^E    ARC. 


3.   SITMINIARV  OF  RESULTvS  FOR   L 

.\TITITDE- 

-continuei 

, 

No. 

Name  i}i  station. 

State 

K 

esult 
atitu 

niii            I'robable  error 
de.                  of  result. 

0 

/ 

// 

// 

30 

Priiicipio 

Md. 

39 

35 

32  -81 

±0  -04 

31 

Maryland  Heitjlits 

Md. 

39 

20 

32  -10 

0  -04 

32 

Pooles  Islaiiil 

Md. 

39 

17 

■7-52 

0-15 

33 

vSugar  Loaf 

Md. 

39 

15 

4971 

0  -K) 

34 

Dover 

Del. 

39 

09 

13  -62 

0  -06 

35 

Webb 

Md. 

39 

"5 

25  -21 

0  -04 

36 

Soper 

Md. 

39 

05 

10 -69 

0  -09 

37 

Rockville 

Md. 

39 

05 

'f45 

0-03 

38 

Taylor 

Md. 

38 

59 

46  -oS 

0  -12 

39 

Strasbury; 

Va. 

38 

59 

31  '49 

0-09 

40 

Cape  Ma\- 

N.J. 

38 

55 

44  74 

0  -06 

41 

Causten,  Washington 

D.  C. 

38 

55 

32-18 

G  -06 

42 

Naval  Observatory  (new),  Washington* 

D.  C. 

38 

55 

13-91 

0  -06 

43 

Hill 

Md. 

38 

53 

52-31 

0-05 

44 

Naval  01)servatory  (old).  Washington  t 

D.  C. 

38 

53 

38  -79 

0-03 

45 

Seaton,  Washington 

I).  C. 

38 

53 

25  -20 

0-15 

46 

Coast  and  Geodetic  Snrvej-  Office,  Washington  j 

D.  C. 

38 

53 

07  -43 

0  -02 

47 

Bull  Run 

Va. 

38 

52 

56-79 

0  -07 

48 

Marriott 

Md. 

38 

52 

25-12 

0  -06 

49 

Cape  Henlopen 

Del. 

38 

46 

40  -00 

0-05 

50 

Clark 

Va. 

38 

kS 

39  -80 

0  -06 

51 

Elliott  Knob 

Va. 

38 

09 

57-51 

0  -11 

52 

Charlottesville 

Va. 

38 

02 

00-95 

0-14 

53 

Long  Mountain 

Va. 

37 

17 

28-72 

0  -09 

54 

Moore 

N.  C. 

36 

23 

54-95 

0  -09 

55 

Young 

N.  C. 

35 

44 

21   -50 

0  -12 

56 

King 

N.  C. 

35 

12 

13  -31 

0  -07 

57 

Paris 

vS.  c. 

34 

56 

3  I  -96 

0-07 

58 

Currahee 

Ga. 

34 

3' 

37  '75 

0  -oS 

59 

Lavender 

Ga. 

34 

19 

15-81 

012 

60 

Sawnee 

Ga. 

34 

J4 

04  -20 

0-08 

61 

Aurora 

Ala. 

34 

08 

47-45 

0-I2 

62 

Atlanta  Middle  Base 

Ga. 

33 

54 

21  -82 

0-05 

63 

Atlanta 

Ga. 

33 

44 

59-30 

(1-12 

64 

Kahatchee 

Ala. 

33 

13 

39  -90 

0  -(-)6 

65 

Montgomery 

Ala. 

32 

22 

45  -41 

0  -04 

66 

Lower  Peach  Tree 

Ala. 

31 

50 

21  -19 

0  -10 

67 

Coon 

Ala. 

31 

'4 

47  -82 

0  -05 

68 

Mobile 

Ala, 

30 

4' 

33-42 

0  -06 

69 

East  Pascagoula 

Miss. 

30 

20 

40-92 

0  -04 

70 

Fort  Morgan 

Ala. 

30 

13 

47  -89 

0-03 

71 

New  Orleans 

La. 

29 

57 

25  -28 

0-07 

*  Center  of  clock-room.                            f  Center  of  small  d 

ome. 

t  station  in  yard. 

B.    THE   RESULTS    FOR   LONGITUDE  AT  THE   ASTRONOMIC  STATIONS 

OF  THE  OBLIQUE  ARC. 

I.    GENERAL    STATEMENT. 

Connected  with  the  arc  there  are  fourteen  well  determined  lon^i^itude  .station.s  avail- 
able for  comparison  of  geodetic  and  a.stronomic  longitude.s.  The  station.s  are  marked 
by  their  appropriate  sign  on  the  general  Map  B  (in  pocket),  and  are  irregularly  dis- 
tributed over  the  region  of  the  arc.  Within  the  limits  of  the  city  of  Washington  there 
are  four  longitude  .stations,  all  within  a  few  kilometers  of  one  another,  and  consequentl)- 
under  the  same  general  influence  of  zenithal  deflection.  The.se  four  stations  have  been 
treated  as  one  in  this  di.scussion.  The  following  stations  are  common  to  the  arc  of  the 
parallel  in  latitude  39°  and  to  the  oblique  arc:  Cape  Ma}-,  New  Jersey;  Dover,  Delaware; 
three*  of  the  Washington,  District  of  Columbia,  .stations;  Stra.sburg,  \'irginia,  and 
Charlottesville,  Virginia. 

The  longitudes  here  given  depend  on  the  standard  longitude  system  of  the  United 
States,  as  presented  in  the  Report  of  the  U.  vS.  Coast  and  Geodetic  .Survey  for  the  year 
1897,  Appendix  No.  2,  "  The  telegraphic  longitude  net  of  the  United  .States  and  its  con- 
nection with  that  of  Europe,  1866-1896.""!'     (pp.  197-261.) 

Six  of  the  arc  stations  are  standard  stations,  i.  e.,  Calais,  Maine;  Cambridge,  Mas.sa- 
chusetts.  Harvard  Observatory;  Cape  May,  New  Jersey;  Wa.shington,  District  of  Colum- 
bia, Naval  Observatory  (old);  Atlanta,  Georgia,  and  New  Orleans,  Louisiana.  For 
these  stations,  particulars  and  full  abstracts  of  the  individual  results  are  given  in  the 
Report  for  1897.  It  .suffices,  therefore,  to  present  only  the  dates  and  results  at  these 
stations,  but  for  the  remaining  stations,  abstracts  are  given  to  the  .same  extent  as  in 
the  Report  for  1897,  together  with  all  necessary  explanation.  In  nearly  every  case  of 
a  telegraphic  determination  of  a  difference  of  longitude  the  ob.servers  exchanged  places 
after  one-half  of  the  proposed  olxservations  had  been  made,  in  order  to  effectively  elimi- 
nate differences  of  personal  equations.  All  these  longitudes  count  from  Greenwich, 
positive  to  the  westward.  The  prol)al)le  error  of  anj-  one  of  the  adjusted  standard  longi- 
tude determinations  is  ±o''o5,  and  none  of  the  probable  errors  of  the  longitudes  used  in 
this  discussion  exceeds  dczo^'og. 


*A  fourth,  named  Seatoii  (ea.st  of   the  United  .States  Capitol),  established  in  1S49.  was  not  a  station  of  sufficient 
importance  to  be  included  in  the  general  longitude  net. 

fKor  an  abstract  of  this  paper  see  Gould's  Astronomical  Journal,  No.  412  ^September  14,  1S97). 


3i8 


THE    EASTERN    OBLIQUE    ARC. 


2.    RESULTvS    FOR    LONGITUDE    PRPIVIOUSLY    PUBLISHED. 

Results  for  longitude  of  stations  forming  part  of  the  standard  longitude  net  of  the  United  States  or 

elosely  eonneeted  thereivith . 

[Taken  from  Coast  and  Geodetic  Survey  Report  for  1897,  p.  254.] 
Name  of  station.  Point  of  reference.  Longitude  west  of  Clreenwich. 

/;.    VI.  S.  °  '  " 

Calais,  Maine.  Transit.  4  29  07  -857  67  16  57  -86 

Caniljridtje,  Massachusetts.  Dome  of  Harvard  College  Observa-  4  44  31  •046  71  07  45  '69 

tor}-. 

Cape  May,  New  Jersey.  Transit.  4  59  43  '045  74  55  45  '68 

Washington,  District  of  Columbia.   Dome  of  old  Naval  Observatory.  5  08  I2'r53  77  o,^  02-30 


Atlanta,  Georgia. 

New  I  )rleans,  Louisiana. 


Tran.sit,  1S96. 


5     37 


338     «4 


23     20  -07 


Transit,    1880   and    1895,     Lafayette  6    00     16763     90     04     II '44 
vSquare. 
Charleston,  vSouth  Carolina.^-  Citadel  Square,  tran.sit.  5     19     44 '076     79     56     01 '14 

Prom  the  .same  Report  we  have  t\\'o  more  of  the  Wa.shington  ,station.s,  pp.  257-259. 
and  261. 


Name  ot  station. 


Point  ot  relerence 


Longitude  west  of  Greenwich. 
h.    1)1.  S.  o  ,  ,, 

Washington,  District  of  Columbia.   Clock-room,  new  Naval  Observatory.   5     08  15784     77     03     5676 

Washington,  Di.strict  of  Colitmbia.   Coast   and   Geodetic   Survey  Office,  5     08  01  709     77     00     25  '64 

transit. 

Results  for  longitude  of  stations  in  the  .Ire  ef  the  Thirty-ninth  /'arallel. 

Name  of  station.  Point  of  reference. 


Dover,  Delaware  f 
Strasburg,  Virginia! 
Charlottesville,  Virginia  1 


Transit,  1897 
Transit,  1S81 
McCormick  Ob.servatorv 


Longitude  west  of  f.reenwich. 

/;.     W.  ,?.  °        "  " 

5     02     05-230         75     3r      18-45 

5     13     26-380         78     21     35-70 


5     14     05  -340 


78     31     20-10 


3.    ABSTRACTS    OK     RESULTS     FOR    DIFFERENCE    OF    LONGITUDE    AND    ADJUSTMENT    OF 

THE    LONGITUDES    OF    THE    REMAINING    STATIONS  X    CONNECTED  WITH    THE    .ARC. 

UIHFERKNCE  OF   LONGITUDE   BETWEEN  BANGOR.'^.   ME.,  AND  CAL.-l/S.  Mlv 


Date. 

Observers  at 

1857. 

Bangor. 

Sept.    18 

23 

,  E.  Goodfellow 

25 

26 

Oct.     10 

G.  W.  Dean 

12 

17 

Difference  of  lonj^itude. 


Calais. 


G.  W.  Dean 


E.  Goodfellow 


w.      5. 
6     00  -275 


Means 


6    00  -275 


6     00  -357 


Bangor  (transit)  west  of  Calais  (transit). 
Longitude  of  Calais, 
Longitude  of  Bangor  (transit), 


00-330 
00  -268 
00  -229  J 
6  00-341 
00  -362 
[         00  -367    I 

//.    in.        s.  s. 

6  00 -316  ±0-015 

4     29  07  -857  ±  o  -05. 

4     35  08-173. 


in.       s. 
6     00-316 


*  'I"his  result  is  added  because  it  i.s  needed  further  on. 

t  These  stations  are  included  in  the  discussion  of  the  arc  of  the  39th  parallel  and  all  nece.ssary  details  are  published 
in  Coast  and  Geodetic  Survey  Special  Publication  No.  4,  "  The  Transcontinental  Triangulation,"  Washington,  D.  C,  1900. 

t  Published  for  the  first  time. 

J  The  longitude  of  this  station  was  differentially  determined  from  Cambridge,  Massachusetts,  in  November  and 
December,  1S51,  lint  the  result  was  found  to  be  weak  and  un.satisfactory.  the  observers  not  interchanging  places,  hence 
no  use  was  made  of  those  observations. 


THK    ASTRONOMIC    MEASURES. 


319 


DIFFERENCF,    OF    LONGITrDK    HICTWKHN    SF.ATihW    STAT/ON*    WASHINGTON- 

o/i.s/cA'yAroA'i'ioi.i)).  wAsiiiNr/roN.  n.  c. 


I».     C.     AM)     .VAI^A/. 


June 


Date, 

1867. 

From 
stg 

western 
nals. 

I'rom 
sig 

eastern 
lals. 

W.-K. 

Mean  western 

and  eastern 

■ignals. 

.( 

V. 

5. 

le        4 

12 

•70 

12 

■67 

+  0  -03 

t2 

•6S 

6 

■6() 

•60 

0  -(X) 

■fx> 

10 

•7c 

•69 

+0  -oi 

•69 

1 1 

■63 

•61 

+  0-02 

•62 

21 

75 

•69 

+  0  '06 

•72 

29 

•6S 

•69 

—0  'OI 

■69 

Mean      12-667 

Observers:  G.  W.  Dean,  in  charge  of  party,  E.  Goodfellow  and  other  observers;  three  were 
engaged  in  the  work  at  the  Naval  Observatory  and  two  at  Seaton,  but  no  interchange  of  obser\-ers 
took  place.  The  results  were  corrected  for  the  personal  equation  of  the  obser\-ers  derived  from  obser- 
vations made  for  this  purpose. 

Naval  Observatory  (Meridian  Circle)  west  of  Seaton  (transit) 

Reduction  to  center  of  dome  at  Observator}^ 

Diflference  of  longitude  Naval  Ob.servatory  (old)  and  Seaton,  transit 

Longitude  of  dome,  Naval  Observatory  (old)  5^' 

Longitude  of  Seaton  ( transit )  5 

Same,  as  adjusted  5 


12* 

■667  inO'  -013 

—0 

■033 

12 

-634  iho"  -013 

oS" 

12' 

■153 

07 

59 

■519 

"7 

59 

■520 

DIFFFRENCp;  OI-'  LONGITUnK  UlsTWKKN  .ST.!  TESl'ILLE.  X.  C,  .\NI)    W ASH [.XGTOX.  D.  C. 


Date. 

1878-79. 


Dec.  19 

23 

24 
25 


Jan. 


Observers  at— 
Statesville.       Washington. 


•E.  Smitl 


G.  W.  Dean 


From  west-  From  east- 
ern or  ern  or 
Statesville   Washing- 
signals,      ton  signals. 


•.S8 
•42 


Mean  of  DitTereiice 

,y  _,.       western    Personal     of  longi-    Weights 


■49 

•57 


-.SI 


o'07 

-0-05 

o  "07 

o'o6 


and  east-   eqnation. 
ern  signals. 

s.     I 
— o'o6 


Weighted  mean 


G.  W.  Dean       E.  Smith 


15 

22  '48 

15 

22  42 

o'o6 

■44 

■39 

0  '05 

.^2 

•20 

0-03 

Weighted  mean 


m. 

5. 

15 

22 -ss 

■56 

•4fi 

■,=;-t 

15 

22  54 

15 

22  -.IS 

■42 

■,^0 

15 

22-42 

4-0-06 


statesville  (transit),  west  of  Washington  (transit), 
Reduction  to  center  of  dome  at  the  old  Naval  Observatorv. 
Statesville  (transit)  west  of  the  dome  of  old  Naval  Ol)st'rvatorv, 
Longitude  of  dome  of  old  Naval  Observatory, 
Longitude  of  vStatesville  (transit), 


tmle. 
J/1 


1     »t 

.V. 

15 

22    52 

•50 

•40 

•48 

15 

22-51 

•48 

■3S 

15 

22-477 

gilts. 

Differ- 
ence. 

. 

s. 
-fo-04 

3 

-1-0 -02 

6 

— 0-08 

6 

O'oo 

9 
16 


O' 


j-n,    22' "477 

^o  -124 

O      15       22    -box 

5    (.\S     12-1 53 
5    23     34  -754 


+0  '03 

O'OO 
— 0-I3 


*'rhis  station  was  established  in  1849,  to  be  used  in  place  of  the  United  States  Naval  Obser\ator>-.  where  it  was 
foinid  both  inconvenient  and  nn.satisfactory  to  make  observations,  as  it  interfered  with  the  regular  duties  of  the  obser- 
vatory staff.  It  was  located  east  of  the  Capitol,  in  an  open  field,  on  Fifth  street  east,  near  A  street  north,  now  covered 
by  buildings.  Telegraphic  connection  with  the  Naval  OUser\'atory  lold)  was  made  in  1867:  distance  V>y  wire.  5J5  kilo- 
meters, or  i%  statute  miles,  nearly. 


;20 


THE    EASTERN    OBLIQUE    ARC. 


No.  3S. 


aSeatoTi 
yWashingtoJx,  JD.  C,  Obs 


Petershujrg 


•  New  Orleo-Tis,  Lcl. 


In  order  to  reach  the  longitudes  of  Mont- 
gomery, Lower  Peach  Tree,  and  Mobile,  Ala- 
bama, it  was  necessary  to  make  a  special  adjust- 
ment of  certain  intermediary  longitude  stations, 
which  bind  them  together  and  connect  them  with 
the  standard  net.  They  are  Petersburg,  Virginia, 
1S52;  Raleigh,  North  Carolina,  1853;  Charleston, 
South  Carolina,  1853;  Wilmington,  North  Caro- 
lina, 1854  and  1856;  Columbia,  vSouth  Carolina, 
1854  and  1856;  Macon,  Georgia,  1855;  Mont- 
gomery, Alabama,  1856;  Lower  Peach  Tree, 
Alabama,  1857,  ^"<^  Mobile.  Alabama,  1857  and 
1858.* 
DiFFERENCK  OF  i^ongitudf:  betwef:n  pf.tersburg, 

VA.,  AND  SEA  TON  STA  TfUN,     D.  C. 


Date, 
1852. 

July  7 

9 

21 

22 

Aug.     2 

7 


Number  of 

Diffe 

rence  of 

stars. 

loii 
111. 

sit 

ufle. 

15 

I 

35 

•5S3 

21 

•636 

13 

■617 

6  and  14 

■559 

9 

•545 

17 

•597 

— 

— 

Mean 


I  35  '589     ±0  -009 


The  observer.s  were  A.  D.  Bache  and  G.  W.  Dean, 
at  Petersburg,  and  L.  F.  Pourtales,  at  Seaton  vStation. 
The  observers  did  not  interchange  places.  Their  per- 
sonal equations  were  ascertained  by  direct  observations 
taken  at  various  times.  The  results,  as  given  here,  are 
corrected  accordingly.  Giving  weights  to  the  individual 
results  in  proportion  to  the  number  of  .stars  olxserved  each 
night,  we  get  JA=i'"  35'*-59i±o'-o22o. 

Petersburg  (transit)  west  of  Seaton   (tran,sit),  i'"  35'^-59i 

±tf"022. 

DIIFEKENCE  OF  I,ONGITUDE  BETWEEN    RALEIGH.  N.  C. 
AND  SEATON  STATION,  D.  C. 


Date. 

Number  of 
stars. 

Difference  of 
longitude. 

IS53- 

;//.         5. 

\pr.     21 

5 

6     32742 

26 

23 

■992 

28 

23 

•S94 

30 

16 

■987 

Mean 

6    32  -904: 

Weightec 

1  mean 

6    32-87.: 

rO  '044 


The    observers    were    B.   A.    Gould  at  Raleigh  and 


*  Details  at  these  stations  published  for  the   first  time.     .See 
also  report   by   Dr.  B.  A.   Gould    in  Coast  Survey    Report  for  I664_ 
J       Appendix  No.  12,  pp.  115,  u6. 


THE    ASTRONOMIC    MHASURKS. 


321 


Iv.  F.   I'ourtales  at  Scaloii    Station.     The   personal  equation   correction  was  deterniineil  from  flirecl 
and  indirect  comparisons.     The  results  given  here  are  corrected  accordingly.* 
Raleigh  (transit)  west  of  Seaton  ftransit)  6"'  32"'873z!=o"044. 


DIKKERKNCK  OF  LONCHTUUK  liKTWKKN   CI  I A  N  I.IISTO.X .   S.  C,   AND  KALICIGJI,   X.  C. 
Date. 


Nvimbcr  (;f 
stars. 


DilTerc-iice  of 
longitude-. 


1853- 
Apr.     29 
May       6 
14 


3 
15 
13 


in.       s. 
5      1 2  '007 

•061 

■164 


Mean 


5       12  -077 -^rO -031 

Observers:  At  Charleston,  L.  R.  Oihhes;  at  Raleigh,  H.  .\.  Could.      The  personal   equation  cor- 
rection being  unknown,  the  probable  error  of  the  result  is  raised  toxo~"i5. 

Charleston,  Gibbes  Ob.servatory  (transit)  west  of  Raleigh  (transit)  5"'i2--  oSir^o'-is. 

Reduction  of  Gibbes  Observatory  to  Citadel  Square  (transit)  at  Charleston. t  ""'396. 

Charleston,  Citadel  Square  (transit)  west  of  Raleigh  (transit)  5'"  i  r-6S4:irO"i5o. 

DIHFKRKNCK  f)F  I.ONGn'lTDF:  BKTWKKN    llll.MiyCTO.W   .N'.  C,   .\ND  I'lyi'l-RSISI  RC .   V.\ 

pifTereiice       Diffi-rciice  of  longitude  referrtd 
of  loiijjitiidc.  to  D-t  and  I'.;  and  means. 


i:  '213        2     \\  244 


Date. 

N 

11  in  her 

01 

servers 

al- 

_ 

0 

'  stars. 

Wilmington. 

I'etersbniK 

1854. 

May     8 

4 

G 

W.  Dean. 

B. 

A. 

Gould. 

27 

"    1 

0. 
A. 

W.  Dean. 
D.  Bache. 

|... 

F. 

Hourtales. 

June    5 

24 

C", 

W.  Dean. 

I, 

F. 

Pourtales. 

14 

•^        1 

27 


L.  F.  Pourtales. 


G.  W.  Dean. 


■239 
■239 

■451 
•4S0 
■449 
■399 


■219 


■9(2     u-2,M 

239  J 


2     1 1 '445 


2     1 1 -540 


Wilmington  (transit)  west  of  Petersburg  (transit),;^    2'"  1  i'"340ii=o*"o33. 
diffkrkncf;  of  uingitude  bf;twef;n  colimkia.  s.  c  .  -\nd  kaleich.  n.  c. 

Mean  J  A 


Date. 

Number 

observers  a 

t— 

of  .stars. 

Colinnhia. 

1S54. 

Jan       21 
Feb.       5 

23 

14 

1 
J 

B.  A.  Gould. 

G.  W 

Dean 

21 

2.^ 

1 

G.  W.  Dean. 

B.  A. 

Gould 

Mar.     12 

10 

1 

Kaleigli. 


Difference  of 
longitude. 


9  3,=;  821  V 
36  '064  j 

9  35-7S7  1 
3.S-779I 


9    35  "942 


I9    35  562  ±  OS  041 


9    35 '9^3 

Columbia  (transit)  west  of  Raleigh  (transit) J    9'"  35''\S62=to''-04i. 

*  F'or  further  remarks  on  the  methods  used  at  this  and  some  other  stations  representing  the  stage  of  the  develop- 
ment of  telegraphic  longitude  determinations,  see  Coast  Survey  Report  for  1S53.  pp.  56-57.  .\  part  of  the  work  done  at 
Raleigh  is  used  as  an  example  of  a  method  for  determining  differences  of  longitude,  in  Vol.  1  of  Chauvenefs  Spherical 
and  Practical  Astronomy,  5th  edition,  1SS7. 

t'riie  observation  for  difference  of  longitude  of  Charleston,  South  Carolina,  and  Sealon  Station.  District  of 
Columbia,  in  February,  1S50,  was  experimental  in  character,  and  too  weak  for  use  here. 

ID.  for  Dean  an<l  P.  for  Pourtales. 

•i  See  remarks  by  Dr.  Gould  in  Coast  Survey  Report  for  i\S4.  PP.  45.  5".  5i,  55.  5^.  and  *123-*133.  for  Raleigh  and 
Columbia. 

4192 No.    7 OJ 21 


IK56. 

Jan.      9 


16 
Feb.    10 


Date. 

1856. 

Mar.  23 

Apr.     3 

7 

S 


24 


Nuinher 
of  stars. 


Date. 

■S53 
Jan.    16 

18 
Feb.     S 

14 


Mar.     9     1         21 


THE    EASTERN    OBLIQUE    ARC. 
diffkki<:nck  oh  i,oN<u'ruDH;  bet\vf::en  macon.  ga.,  .^xd  Columbia,  s.  c. 

Mean  A  A. 


Ob.servers  at — 
Macon.  Cobimbia. 


Difference  c 
longitude. 


C.  W.  Dean. 


K.  (iooflfellow. 


H.  <  ioodfellow. 


C.  W.  Dean. 


10  22-205. 
■,SiS 
■380 

10     22 '029 

21  '963 

22  '059 
^3-479 


10     22 '368 


10       22    132 


10      22 '250  +  0   O.SI 


Macon  (transit)  west  of  Coluni1)ia  (transit),     10'"  22^"2sc>  rt  o-"05i. 
DIFFHRKN'CF:  of   LONGITUUK  KK'rWKF;X   CCIJ'MJI/A.  S.  C.  AND    I!'lLML\'GTO.V.  N.  C. 

Mean  J  A. 


Nvnnber 
of  stars. 


( )bservers  at — 
Columbia.  Wilniiuifton. 


Difference  ut 
longitude. 


C.  W.  Dean. 


K.  Goodfellow. 


12     21  74^ 

■744 

•878 

■6S0  I 
12     21740  I        ,_, 

■660  I 


12     21762 


12     21  731+0028 


K.  Goodfellow.  G.  W.  Dean.  1      ''       '   '"'    I        '-     21700 

Coluinl)ia  ( tran.sit )  we.st  of  Wilniiiixton  (transits     12'"  2l'"73l  =bo*'o2.S. 

DIFFKRKNCK  OF  l^oNGITfUF,   BF:T\VEF.N  A/iKVTGOM/-:/^  i'.  AI<A.,  AND  ArACO.X.  GA. 


Number 
of  stars. 


( >bservers  at- 


23 
30 


Montttomerv. 


(i.  W.  Dean. 


F".  Goodfellow. 


E.  Goodfellow. 


G.  W,  Dean. 


Difference  of 
longitude, 

III .       i. 

110  41  568  1 
■501  I 
■S69  I 
•488  J 
110  41  727  J 
■595  I 
595  I 
■520  ) 


Mean  A  A. 


10  41 '609 


10     41 -570  +  0  015 


MonlKOinery  (transit)  -west  of  Macon  (transit),     10'"  4l'''570  dzC-ois. 
DIHFEKENCE  OF   [.oNGITtTDK   HFTWEEN   LOll'/Ck  PI-.ACH  TREE.   Al.A.,  AND  MO.WGOM  ER  V.  .\\A. 


Date. 

Apr.  2 
6 
7 
10 
19 
20 
23 
28 


Ol)servers  at — 
l,ower  Peach  Tree.  Montgomery 


31 
14 

13 
3' 
26 

18 


(',.  \V.  Dean. 


E,  Goodfellow. 


E.  Goodfellow. 


G.  W.  Dean. 


Difference  of 
longitude. 


4  5^ '79-^ 
■7-'3 
■736 
■943 

4  58790 
79.=; 
■752 
■774 


Mean  J  A. 


4     5S -Soo 


4     5877S 


III.         i. 


4     5S-789io-oi6 


Lower  Peach  Tree  (transit)  west  >.>{  Montgomery  (transit),    4'"  sS^'ySQ  io^-oi6. 


THE    ASTRONOMIC    MEASURES. 


32: 


DiKFKRKNCK  OH  r/)Nr,rrfi)i<;  hi<'.twi<:kn  lyroiuij-:^  ai.a  ,  and  i.invi:K  I'Eacii  irei-:  .\\.\ 


Dat 

c. 

Nunil 
of  sta 

ler 
rs. 

Mobile-. 

'S57- 

May 

21 

34 

24 
25 

3S 
22 

C.  W    Dean. 

26 

34 

June 

2 

41 

6 

1 1 

Iv  Cioodlellow 

7 

3^ 

ohservtrs  al —  Uiffcrencc  of 

I<ower  I'each  Tret.        loiiKitude. 


m.       i, 
I     5y  795 
73" 
■'^37 


Mean  Ak. 


K.  Ooodfellow 


;.l/ 


;« ,     i. 
'     59  730 


C  W.  I)e 


,J 


I     59  'S^ig 

•7S6  \        I     59 -sort 
742 


I     59  7&'i   ±o'Qi6 


Mobile  (transit)  west  of  Ivower  I'each  Tree  (transit)  i'"  59^768  •:o"oi6. 

DIHf'EKKNCl-;  ()!•    I.ONC.  ITIDK   BF,l\VlCl-;\  Nh.W  OKLJiA.WS.  1,A..  AM)  MOIUI.E.  AI,A. 


Date 

Number 
of  stars. 

New  Orleans. 

185S 

Jan. 

'9 

7 

Feb. 

H 

12 

'5 
16 

IS 
22 

•  H.  (ioodfellow 

17 

32 

■9 

3« 

Mar. 

I 

3" 

26 

23 

0,  \V,  Dean. 

Apr. 

2 

i.S 

observers  at- 


DifTercnce  of 
.Mobile.  lonsiitnde. 


Mean  AX. 


D.*  and  M.* 

^     07  01 2 

I). 

07  '075 

I),    and  M. 
I),    and  M. 

06  -953 

07 -022 

S 

07  'o^s 

M. 

07 '079 

>«.      I 

s. 

D.    and  M. 

07  '074 

s     07 

147    3:0  *o 

\ 

^      07 '396 

E.  Cioodfellow   j 

■230 

s 

o7-256_ 

I 

•141 

New  Orleans,  Basin  street,  west  of  Mobile  (transit),  8'"     07"i47iho"'022. 

Reduction  to  station  Lafayette  Square  —  o  '866. 

AX  New  Orleans,  Lafayette  vSquare,  anil  Mobile  S       06  '281:110  '022. 

Adjustuiciit  of  S((0)idarv  tclcorapliic  lonoitiidc  sta/ioiis  to  tlic  sttx)idard  tcUffraphic  longitndt 

net  of  tlic  rnitcd  Slates. 

Referring  to  the  preceding-  diagram ,  wliich  shows  the  connection  of  the  longitude  sta- 
tions between  Washington  and  New  Orleans,  it  is  seen  that  the  three  circuits  de  nand  as 
man}-  conditions  to  be  satisfied.  The  conditional  or  observation  equations  are  established 
as  foUowsf: 


AX  New  Orleans  and  Mobile 

A\  Mobile  and  Lower  Peach  Tree 

AX  Lower  Peach  Tree  and  Montgomery 

A\  Montgomery  and  Macon 

AX  Macon  and  Columbia 

AX  Colnniliia  and  Raleigh 

AX  Raleigh  and  vSeatou 

AX  Seaton  and  Washington  (Old  Naval  Observatory) 


m. 

8 

J.l 
06  '281 

Corrections. 

* 
(1) 

I 
P 

5 

I 

59  768 

(2) 

3 

4 

5'^  -7X9 

(3) 

3 

10 

41  •57'i 

(4) 

2 

10 

22  -250 

i5) 

26 

9 

35  •-'^62 

(6) 

>7 

6 

3-'  -^7:. 

(7) 

'9 

-0 

1 2  634 

iS) 

-' 

-2     52     04  759 


*■  Y>.  stands  for  ('..  W.  Dean  anil  M,  for  A.  T.  Mosnian. 


t'rhe  nnnibers  in  coUnnn     .    eiinal  ioihx->  times  the  sijuare  of  prolxible  errvir. 


,24 


THE   EASTERN   OBLIQUE    ARC. 


True  value  iu  standard  system  52'"  04''6io,  hence  the  first  observation  equation: 

o=+o-i49+(i)^(2)  +  (3)  +  (4)  +  (5)  +  (6)  +  (7)-(S) 


J  A      Columbia  and  Wilmington 
JA      Wilmington  and  Petersburg 
JX      Petersburg  and  Seaton 


JA      Raleigh  and  Seaton 
//A      Columbia  and  Raleigh 


hence  the  second  equation: 


12 

21  731 

(9) 

8 

2 

1 1  -340 

(10) 

II 

I 

35  -591 

(II) 

5 

16 

oS  -662 

>n. 

.'^. 

6 

32  -873 

(7) 

19 

9 

35  -862 

(6) 

17 

16 

oS  735 

o=+o-o73+(6)  +  (7)-(9)-(io)-(ii) 


JA       Charleston  and  Raleigh 

JA      Raleigh  and  Seaton 

J  A      vSeaton  and  Washington  (Old  Naval  Observatory) 


5     11-684 

(12) 

225 

6    32-873 

(7) 

19 

-0     12  -634 

(8) 

2 

3    II    31-923 


True  J/A.  in  standard  s^^stem  11"  3i''923,  hence  third  equation 

o=o^-ooo— (12)  —  (7)  + (8) 

Normal  equations. 


Correlate  equal 

'ens. 

Corr. 

I 

7 

c, 

c. 

c. 

(I) 

5 

+1 

(2) 

3 

+1 

(3) 

3 

+1 

(4) 

2 

+1 

(5) 
(6) 

26 

+  1. . . 

17 

+1 

+  1 

(7) 

19 

+1 

+  1 

—  I 

(8) 

2 

—  I 

+  1 

(9) 

s 

—  I 

(10) 
(II) 

1 1 

.  .  —  I . . 

5 

—  I 

(12) 

225 

—  I 

0=4-0 

•149     +77C,+36C. 

-21C3 

o=+o 

■073     +36C,+6oC. 

-19C3 

0^     0 

•000     —  21C1 

-I9C. 

+  246C3 

Cx  =  - 

-o-ooi  93 

c.=- 

-Q-OOO    11 

C3=- 

-0  -QOO    17 

5. 

5. 

(I)=- 

-0  -0096 

(7)  = 

=  -0-0355 

(2)       - 

-0  -0058 

(8) 

4-0  -0035 

(3)     - 

-0  -0058 

(9) 

4-0  -0009 

(4)     - 

-0  -0039 

(10) 

+0  -0012 

(5)     - 

-0  -0502 

(II) 

4-0-0006 

(6)     - 

-0  -0347 

(12) 

+0  -0383 

/.      IH. 

i. 

5     oX 

'2-153 
1 2  -6375 

77 

tJ3 

"2  -295 

5     07 

59 '5155 

76 

59 

52  73^ 

+   I 

35  -59'^ 

5     f^ 

35  'K'?' 

77 

23 

46 -Sot 

4-   2 

II  -3412 

5     II 

46  -4483 

77 

56 

36  724 

+  12 

217319 

5     24 

C)S  •i8<)2 

Si 

02 

02  703 

THK    y\STRONOMIC    MEASURES.  325 

kesultinfT  longitudes. 

A  Washiiifi^ton,  Old  Naval  ( Jhservalory  Dome 
AX  Washinj^toii  and  Seatoii 

\  Seatoii  ( transit ) 
A\  Seaton   and  I'L-tersbur}^ 

A  Petersburg  (transit  ) 
AX  Petersburg  and  Wihniugton 

A   Wilmington  (transit) 
AX   Wilmington  and  Columbia 

A  Columbia  (transit ) 
Check: 
AX  Seaton  and  Raleigh  +  6     32  '8375 

A  Raleigh  (transit )  5     14     323530     78     38     05-295 

AX  Raleigh  and  Columbia  -f  9     35  ''''273 

\   Columbia  (transit )  5     24     08  ■1S03     81     02     02704 

Further — 

JA   Columbia  and  Macon  -)-io  22 '1998 

A  Macon  (transit)  5     34  30-3801     83     37     35  •7or 

AX  Macon  and  Montgomery  -(-10  41  -5661 

A  Montgomery  (transit)  5     45  11  -9462     86      17     59-193 

AX  Montgomery  and  Lower  Peach  Tree  +  4  58  '7832 

A  Lower  Peach  Tree  ( transit )  5     50  1(1-7294     87     32     40-941 

AX   Lower  Peach  Tree  and  Mobile  -\-   i  59  -7622 

A  Mobile  (transit)  5     52  10-4916     88     02     37-374 

AX  Mobile  and  New  Orleans,  Lafayette  Square      -)-   8  1)6-2714 

A  New  Orleans,  Lafayette  Square  6     00  16-7630     90     04      11  -445 

If  the  above  results  are  compared  with  those  obtained  in  tlie  prehnhnar_\-  adjust- 
ment of  the  telegraphic  longtitnde  system  as  it  stood  in  1884,-'-  it  will  be  .seen  that  the 
present  longittides  are  al)out  one-tenth  of  a  second  of  time  greater  than  those  fottnd  in 
1884.  This  is  mainly  dtte  to  the  introduction  into  the  system  of  tlie  fourth  cable  line 
across  the  Atlantic  Ocean  in  1892. 

The  probable  errors  given  in  the  stunmar}-  of  restilts  are  close  approximations. 


*  Report  of  1884,  Appendix  No.  11,  pp.  407-430;  and  Report  for  1S97,  .\ppeiidix  No.  2,  pp.  197-261. 


320 


THE    EASTERN    OBLIQUE    ARC. 

4.    SUMMARY   OF    RESULTS    FOR    LONGITUDE. 


No. 


10 
II 


13 
14 

]6 

17 


Calais 

Bangor,  Thomas  Hill 

Cambridge,  Harvard  Observatory 

Cape  May 

Dover 

Washington,  Seaton  Station 

Washington,   Coast  and  Geodetic  Survey 

Office 
Washington,  Naval  Observatory  (old) 
Washington,  Naval  Observatory  (new) 
Petersburg,  Roslyn  Station 
Wilmington,  De  Rosset  Station 
Strasburg 
Charlottesville 

Raleigh,  vState  House  Grounds 
'  Charleston,  Citadel  Square 
Statesville,  near  Simenton  College 
Columbia,  Capitol  Square 
Macon,  Academy  Square 
Atlanta 

Montgomery,  Capitol  Hill 
Lower  Peach  Tree,  Wilson  County 
Mobile,  Public  Square 
New  Orleans,  1895,  I<afayette  Square 


state. 

Referred  to. 

I 

,on8ritn<ie 

Probable 
error. 

0 

/ 

// 

// 

Me. 

Transit 

67 

16 

57-86 

±0-75 

Me. 

Tran.sit 

68 

47 

02  "60 

0-7S 

Mass. 

Dome 

71 

07 

45  69 

0-75 

N.J. 

Transit 

74 

55 

45-68 

075 

Del. 

Transit 

75 

31 

18  -45 

079 

D.  C. 

Transit 

76 

59 

52-73 

0-78 

D.  C. 

Transit 

77 

00 

25-64 

0-78 

D.  C. 

Dome 

77 

03 

02-30 

0  -75 

D.  C. 

Clock-Room 

77 

03 

56-76 

0-78 

Va. 

Transit 

77 

23 

46-61 

0  -84 

N.  C. 

Transit 

77 

56 

36  -72 

I  -Q 

Va. 

Transit 

7S 

21 

35-70 

0-80 

Va. 

Observatory 

7S 

31 

20  -lo 

0  -80 

N.  C. 

Transit 

78 

38 

05-30 

I  -o 

S.  C. 

Transit 

79 

56 

01  -14 

0-78 

N.  C. 

Transit 

80 

53 

41  -31 

Q  -80 

s.  c. 

Transit 

Si 

02 

02  -70 

I     2 

Ga. 

Transit 

S3 

37 

35-70 

I  '3 

Ga. 

Transit 

84 

23 

20  "07 

o-8o 

Ala. 

Transit 

86 

17 

59-19 

I  -I 

Ala. 

Transit 

87 

32 

40-94 

I   I 

Ala. 

Transit 

88 

02 

37-37 

I  -Q 

La. 

Transit 

90 

04 

II  -44 

o-So 

C.     RESULTS  FOR  AZIMUTH  AT  THE  ASTRONOMIC  STATIONS  OF  THE 

OBLIQUE  ARC. 

The  stations  where  an  azimuth  was  deternuned  astroncjniically  are  (juite  munerous 
and  are  distributed  over  the  whole  extent  of   the  arc.      There  are  56  azimuth  stations, 
J  14  of  which  are   in  roiii})io>i  with   the  arc  of  the  parallel  in  latitude  39.      All  necessary 

details  in  regard  to  the  observations  at  these  stations  are  given  in  the  ])ublished  di.scu.s- 
sion  of  that  arc.  vSome  of  the  particulars  are  repul^li.shed  in  this  discussion  in  the  proper 
place. 

The  various  methods  employed  by  the  Coast  and  Geodetic  vSurve\'  for  the  determi- 
nation of  azimuths,  together  with  the  required  formuke  and  their  numerical  application, 
are  .so  fully  set  forth  in  Appendix  No.  14,  Coast  and  Geodetic  Survey  Report  for  1880, 
pp.  261-286,  and  in  a  later  edition,  Appendix  No.  7,  Coa.st  and  Geodetic  Survey 
Report  for  1897-98,  pp.  377-407,  that  no  further  reference  is  required.  It  will  suffice 
for  a  full  exhibit  of  the  azinuithal  results  to  present  for  each  station  the  following  par- 
ticulars— the  method  employed,  instrument  u.sed,  stars  observed,  the  arrangement  and 
composition  of  sets  of  observations,  the  number  of  measures  and  position  of  circle  or 
instrument,  and  any  other  details  pertaining  to  the  operation;  the  names  of  the  observers, 
and,  finally,  the  individual  results  in  the  form  of  an  abstract,  together  with  their  prob- 
able errors. 

The  apparent  places  of  stars  are  taken  directly  from  the  American  Ephemeris  or 
derived  from  Gould's  "Standard  Places  of  Fundamental  Stars,"  Washington,  1S66 
(.second  edition),  except  in  a  very  few  cases. 

The  probable  error  of  the  result  of  a  .single  .set  and  that  for  the  resulting  azimuth 
of  the  mark  are  due  to  ob.serving  errors  and  exclude  the  probable  error  in  the  star's 
catalogue  place.  When  referring  the  azimuth  of  the  mark  to  the  triangulation,  the 
probable  error  of  the  referring  angle  is  not  given,  as  in  general  it  is  not  accurately 
determinable.  The  local  adjustment  of  the  horizontal  directions  at  a  station  include 
that  of  the  mark,  and  the  angle  between  the  mark  and  the  direction  of  a  line  in  the 
triangulation  was  corrected  l)y  applying  to  it  the  iincni  shift  or  average  correction  to 
all  the  directions  at  the  .station  in  the  .second  or  figure  adjustment.  The  j^robable  error 
of  any  resulting  azinuith  of  a  line  in  the  triangulation  may  l)e  estimated  as  not  less 
than  one-half  of  a  second.  One-third  of  a  second  lias  l)een  taken  for  the  probable 
error  of  an  observed  direction,  resulting  from  the  figure  adju.stment,  whence  dto""47 
for  the  angle  "mark  and  line."  Coml)ining  this  with  ±o"'25  as  the  proliable  error 
of  the  mea.sure  of  the  azinuith  of  the  mark,  we  get  ±o"'53  for  an  approximation  oi  the 
probable  error  of  a  resulting  azinuith  of  a  line.  For  ordinary  or  le.^^s  preci.se  work  this 
value  may  rise  to  three-fourths  of  a  second. 

327 


328 


THE    EASTERN    OBIJOUE    ARC. 


(p  =  44     59    2. 


I.  COOPER,  Maine:. 


A  =  67°   2S''i  west  of  Greenwich. 


The  75'"'  direction  theodolite  No.  i  (Troughton  &  Simms)  was  mounted  over  the 
triangulation  .station.  Focal  length  of  telescope,  115  centimeters;  clear  aperture,  7'5 
centimeters.  The  azimuth  mark  was  located  upon  a  hill  to  the  north  of  the  station  and 
distant  about  2  miles.  Light  was  shown  through  an  aperture  three-fourths  of  an  inch  in 
diameter;  for  day  observations  a  wand  i  foot  in  length  and  i  inch  in  breadth  was  placed 
above  the  center  of  the  aperture.  A  set  of  observations  on  Polaris  generally  consisted 
of  3  observations  of  the  mark,  telescope  direct,  and  3  observations  telescope  reversed, 
followed  by  5  observations  of  the  star,  with  the  necessary  time  and  level  record;  the 
instrument  was  then  reversed  and  the  observations  were  repeated  in  the  reverse  order. 
In  ca.se  of  A  Ursae  Minoris  6  observations  were  made  upon  the  star  both  before  and 
after  reversal.  One  division  of  level  =  i"'43.  Ob.servers,  G.  W.  Dean  and  R.  E. 
Halter.      Probable  error  of  a  .single  result  for  azimuth  ±  o"'Scj. 

Siinimary  of  7'esults  for  aziuinth  al  Cooper,  Maine. 


Date. 

1859. 

Polaris  near  eastern  elongation 
Position.           ,Mark^                  ^ 

A  frsa; 
Date. 

I^i9- 

Minoris  near 
Position. 

upper  culmination. 
Mark                       . 
W.  of  N.                  ^ 

C         '             "                                     " 

Sept.    9 

IV                 2  49  47-53 

+0  -85 

Sept. 

9 

\\ 

2  49  47 '49 

+ 1  -50 

12 

V                            48  -06 

+0-32 

12 

\ 

47 '94 

+  1  -OS 

14 

I                             50  -07 

-1-69 

14 

I 

49-09 

~o  -10 

15 

II                            46-58 

+  1  -80 

15 

II 

50  -69 

—  I  -70 

16 

III                           47 -So 

+0-58 

16 

III 

47  '93 

+  1  -06 

iS 

III                           49-08 

— 0-70 

18 

IV 

50  -82 

-I  83 

19 

V                           49  '56 

-I  -18 
•31 

Mean 

2  49  48-99  +  0 

Mean         2  49  4S-3S  +  1. 

■40 

0 

/          // 

Mean  of  groups 
Diurnal  aberration 

2  49  48  -68 

-0-31 

Azimuth  of  Mark 

17 

7   10   n  -63 

-_ho"-25 

Angle  between  Mark 

\\\A  Howard 

IS 

5    16  59 'SS 

Azimuth  of  Howard 

35 

t  53   12 '05 

2. 

HOWARD 

,   MAINK. 

(p  =  44°37'-8  \  =  67=23' -S 

Theodolite  No.  i  was  mounted  over  the  station.  The  mark  was  located  upon  a  hill 
about  I  Yz  miles  north  of  the  station.  Light  was  shown  through  an  aperture  three-fourths 
of  an  inch  in  diameter;  a  wand  i  foot  high  and  i  inch  wide  was  placed  above  the  aperture 
to  ser\'e  as  day  mark.  In  the  case  of  Polaris  a  set  of  observations  consisted  of  3  pointings 
on  the  mark  with  telescope  direct,  3  pointings  on  the  mark  with  telescope  reversed, 
followed  by  5  pointings  on  the  star,  or  6  in  case  of  S  ITrsae  Minoris,  with  the  necessary 
level  and  time  records;  the  instrument  was  then  reversed  and  the  above  obsei^'ations 
were  repeated  in  the  reverse  order.  One  division  of  level  =i"'43.  Observers,  G.  W. 
Dean  and  R.  E.  Halter.     Probable  error  of  a  single  result  for  azimuth  rbo"'8o. 


THE   ASTRONOMIC    MEASURES. 


329 


Sininiiaiy  of  results  for  azimullt  at  Harvard .  Maine. 


S  Ursx'  Minoris  iieai-  iij>i)ir  ciilmiiKitioii. 


['rs;c  Minoris  near  eastern  elongation. 


Date. 

rosition. 

K. 

of  N. 

'859- 

0 

, 

,, 

July    iS 

I 

7 

¥> 

<>i  72 

21 

n 

\"^  M 

23 

in 

05  '05 

24 

IV 

0472 

25 
29 

II 

02  ■.« 
05 'IJ 

Mean 
Diurnal  aberration 


7  •1i'>  04 -39  ±0-35 
+0-33 


J 

Date. 

1859. 

I'osition. 

Mark 
K.of  N. 

0    1       " 

d 

-0  '33 

July 

IX 

I 

'.  46  03  35 

4-0-4I 



20 

II 

05  49 

-'•73 

■-o-6f! 

21 

11 

05 '63 

1S7 

-"■33 

23 

III 

04  -.so 

-074 

+  2 '06 

24 

IV 

03'I7 

+059 

-074 

25 

V 

03  46 

+030 

28 

V 

03  43 

+0-33 

29 

I 

01  72 

f2-04 

Aug. 

6 

IV 

02-84 

+092 

M 

S 
^-an 

III 

04  00 

-024 

7  46  0376  iO 

•25 

Dinrna 

aberration 

^031 

Mean  of  j^roups 

Azirutth  of  Mark 

Angle  between  Mark  ami  Pigeon 

Azimuth  of  Piycoii 


7  46  04  •40 
1S7   46  04  ■40rtzo"  -27 
123   51    19   29 
63  54  45  •  " 


3.    HUMPK.\CK,   M.VIXK. 

(p  =  44°  5i'-.S  A  =  6S°o6'-6. 

Theodolite  No.  i  was  mounted  over  the  trigonometric  s'ation.  The  mark  wa.s 
located  in  an  open  field  estimated  to  be  about  2  miles  from  the  station,  light  was  shown 
through  an  aperture  three-fourths  of  an  inch  in  diameter,  and  for  day  observations  a 
wand  I  foot  high  and  i  inch  wide  was  placed  vertically  above  it.  A  set  of  observations 
consisted  of  3  pointings  on  the  mark,  telescope  direct,  and  3  jiointings  telescope  reversed, 
5  pointings  on  the  star  for  a  Ursae  Minoris  and  6  for  S  Ursie  Minoris.  The  instru- 
ment was  then  reversed  and  the  observations  were  repeated  in  the  re\-erstj  order;  the 
necessary  time  and  level  records  were  made  for  ])oth  positions  t)f  the  instrument.  One 
division  of  level  =  i"'43.  Ob.server,  G.  \V.  Dean.  Prol)able  error  of  a  .single  result  for 
azimuth  zfc  o"'86. 

Suiinitary  (f  results  for  a::iiiiiit/i  at  Iliinipback,  Maine. 


S  Ursse  Minori.s  near  upper  culmination. 


aUrsx  Minoris  near  eastern  elongation. 


Date. 

Position. 

Mark 
K.  of  N. 

A 

Date. 

Position 

Mark 
E.  of  N. 

A 

1858. 

0       '        t> 

185S. 

0        '          r/ 

,, 

Aug.    9 

Ill 

114  20   12 '86 

-0 

07 

Aug.    9 

III 

14    20    13    11 

-  1  01 

13 

IV 

'-■•39 

+0 

40 

12 

III 

1 1  -37 

+  073 

14 

\' 

12-51 

+0 

28 

13 

IV 

11  -00 

+  1    10 

16 

I 

11-52 

+  1 

27 

14 

V 

10-71 

•1- '  39 

17 

II 

14  -68 

—  1 
35 

89 

16 
17 
19 
20 
23 

2.S 

I 

II 
II 
IV 
V 

I 

1  1  -63 
'3-65 
14-17 
10-84 
11-13 

'3  '34 

-fo-47 

-2-07 
+  1-26 
+0-07 
-1-24 

Mean 

114  20  12-79  -*^0' 

Mean 

14  20  1210  ±0 

2S 

Diurn 

al  aberratio 

u              +0-33 

Diurna 

aberration 

+0  -31 

0 

'         / 

Mean 

of  groups 

114 

20    12 

76 

AzinuUh  of  Mark 

294 

20    12 

•76r 

£:0"-22 

Anglo 

between  Mark 

a  IK 

C 

ooper         39 

37  40  "40 

Azimuth  of  Cooper 

254  42  52 

36 

*  Reji-oleii  bv  ivirce"s  criterion. 


330 


THE    EASTERN    OBLIQUE    ARC. 


4.    MOUNT    DESERT,   MAINE. 

(?>=44°  2i'-i.  /l=6S°  i3'-6. 

Theodolite  No.  i  was  mounted  over  the  triangulation  station.  The  mark  was 
estabHshed  near  Hulls  Cove,  and  is  distant  from  the  station  about  4  miles.  Light  was 
shown  through  an  aperture  one  inch  in  diameter,  and  above  this  a  wand  was  adjusted 
verticalh'  for  day  observations.  A  set  of  observations  con.sisted  of  3  pointings  on  the 
mark,  telescope  direct,  3  pointings  telescope  reversed,  5  pointings  on  a  UrscC  Minoris  or 
6  on  A  Ursse  Minoris.  The  instrument  was  then  reversed  and  the  observations  were 
repeated  in  reverse  order;  time  and  level  records  were  made  for  both  positions.  One 
division  of  level  i"'53.  Observers,  A.  D.  Bache  and  G.  W.  Dean.  Probable  error  of 
a  single  result  for  azinuith  zh  o"'So. 


Siiiiiiiiary  0/ irsii/ls  for  aziiiut/h  at  i\foHnt  Desert,  Maine. 


a  UrsiL 

Minfjvis,  1 

it-ar  eastern  el< 

)n 

nation. 

A  llrs;e  Minoris, 

near  upper  culmination 

Date. 

PoMtioii. 

Mark 
W.  of  N. 

J 

Da 

te. 

Position. 

Mark 
W.  of  N. 

A 

1S56. 

C        '           " 

,, 

1856. 

0    /      // 

ft 

Aug.  30 

II 

12   19  oS "89 

4-0  -66 

Sept 

I 

II 

12  19  II  -08 

—  I  04 

Sept.    I 

II 

og  '20 

-f  0'3.S 

2 

III 

07  '65 

-f^-39 

2 

III 

09-24 

+  0-31 

3 

IV 

10 -88 

-0-S4 

3 

III 

07-63 

+  1-92 

4 

V 

10  -61 

-0-57 

4 

IV 

09-S9 

--0'34 

7 

I 

08-78 

+  1  -26 

5 

v 

11  -09 

- '  '54 

18 

III 

II  -26 

—  I  -22 

7 

I 

OS -77 

-fo-7S 

9 

I 

10 -S6 

-1-31 

16 

IV 

09  -79 

-0-24 

17 

v 

Mean 

10-10 

to 

-22 

Mean 

12  ]q  og  -55  _ 

12  19  10  04  +  0 

■41 

Mean  of  groups  12  19     0979 
Diurnal  aberration                                                                       --  o'3i 

Azimuth  of  Mark  167  40     50-52±o"-2o 

Angle  between  Mark  and  Ragged  Mountain  S9  10     03  -95 

Azinuith  of  Ragged  iNIountain  7S  30     46  "57 

5.    MOUNT    HARRIS,  M.\INK. 

V  =  44°  39' 'g-  ^  =  69°  o8'-9. 

Theodolite  No.  i  was  mounted  over  the  triangulation  .station.  The  mark  was  located 
upon  the  south  side  of  the  old  stage  road  from  Dixmont  to  Hampden,  about  2^  miles 
from  Dixmont  village;  light  was  shown  through  an  aperture  i  inch  in  diameter,  and  for 
day  observations  a  wand  i  foot  high  and  i  inch  wide  was  placed  over  it;  the  lower  half 
of  this  wand  was  covered  with  black  cotton  cloth  and  the  upper  half  with  white  cotton 
cloth.  A  set  of  ob-servations  con.si.sted  of  3  pointings  on  the  mark,  telescope  direct, 
3  pointings  telescope  reversed,  5  pointings  on  the  star  if  a  Ursae  Minoris  or  6  if  A  Ursse 
Minoris.  The  instriunent  was  then  reversed  and  the  observations  were  repeated  in  the 
reverse  order;  time  and  level  records  were  made  for  both  positions.  One  division  of 
level  =  i"'54-  Observers,  A.  D.  Bache  and  G.  W.  Dean.  Probable  error  of  a  single 
re.sult  for  azimuth  ±  o"'98. 


THK    ASTRONOMIC    MEASURES. 


331 


Siiiiiiiiary  of  rcsu/ls  fur  a-:iinii//i  al  J/uiiii/  If  arris,  Maine. 


atlrsic 

Minori.s  near  eastern  cloiiji: 

li( 

jii 

A  I 

rsie 

Miiioris  ne 

ar  upper  culmination. 

Date. 

I'o.sitioii. 

Mark 
K.  of  N. 

J 

Date. 

ro.sition. 

Mark 
K.  of  N. 

A 

1855- 

0     /        " 

/' 

'S.55 

0    /        " 

" 

Aug.   i9 

V 

62  37  2y32 

1  I  -03 

Aug. 

30 

V 

62  37  30 -y* 

4-1-08 

y> 

V 

29-19 

t-I  -16 

Sept. 

4 

!V 

32 -ss 

-I   19 

Sept.    3 

IV 

3" '25 

1  OK) 

5 

in 

30-68 

+0-98 

^ 

IV 

30 '97 

-  0  62 

6 

n 

32  93 

-1-27 

5 

III 

(26-22]* 

8 

I 

31 -28 

+0-38 

6 

III 

29-68 

fo-67 

S 

II 

29 -es 

1-0 -67 

10 

I 

:,o  -90 

0-5.5 

II 

I 

3?  '47 

-3-12 

12 

II 

31  -4S 

-I-I3 

14 

III 

Mean 

28-62 

■3" 

+ 1  -73 

Mean 

(■'^  37  3"'35±o 

62  37  31  -66±o 

35 

Mfiiii  by  groups 

Diurnal  aberration 

A/.iinnth  of  Mark 

Angle  between  mark  and  Hiinijiback 

A/.inuith  <jf  Humpback 


62  37  31  -«) 

242  37  3'  •3i±o"'25 

■'   57  39 '3' 
254  35    10-62 


6.    KAOOKI)    MOI'NT.AIN,    MAINK. 

(p  =  44°    12'-;.  X  =  69°  09'- 1. 

Theodolite  No.  i  was  mounted  over  the  triangulation  station.  The  mark  was  located 
about  2}^  miles  from  the  station  and  was  arranged  in  the  usual  manner.  A  set  of  obser- 
vations generally  consisted  of  3  pointings  on  the  mark,  telescope  direct.  3  pointings  on 
same,  telescope  reversed,  5  pointings  on  the  .star,  with  time  and  level  record.  The  instru- 
ment was  then  reversed  and  the  observations  repeated  in  reverse  order.  One  division  of 
level  =  I "■54-  Observers,  A.  D.  Bache  and  G.  W.  Dean.  Probable  error  of  a  single 
result  for  azimuth  ±  o""66. 

Siiiiiiiiary  0/  results  for  aziiHK/h  at  A'(ri,';'(-i/  ^/olnllain .  .Uai)it\ 


a  Unsit 

Minoris  near 

e.istern  elon 

Ra 

tioM, 

A  I'rsie 

Miuoris  ue 

ir  upper  culmination. 

Date. 

Position. 

Mark 

K.  of  N. 

'J 

Date. 

Position. 

Mark 
K.  of  X. 

A 

iS54- 

0      /          « 

1, 

1S54. 

0      '          " 

„ 

Aug.   25 

I 

"     53     54  '66 

+  0-2}. 

■^ug.  25 

I 

0    53    56  -00 

~  1    12 

29 

II 

54  '22 

+  0  -67 

.Sept.  15 

IV 

54 -6S 

+  0-20 

.30 

II 

53  '34 

+ 1  '.55 

16 

V 

53  96 

+0-92 

Sept.    .1 

II 

,56  '.W 

-   I  50 

1 1 
.3 

III 
III 

55  ',55 
.^5  'Ss 

0-66 
-0'93 

15 

IV 

54  '00 

+  0-S9 

16 

\- 

.55 '16 

-0-27 

53     .54'S9±o'24 


Mean 


o     53     54  -SR  ±  o  -40 


Mean  bv  group.s 

Diurnal  aberration 

.\/.iniutli  of  Mark 

.\ngle  between  Mark  aiul  Mount  IMea.sant 

Azimuth  of  Mount  Pleasant 


<^  53  54  "^^ 
-03 1 

''*^^  53  55  ■-"  =to"  '^ 

99  05    10  '20 

Si  4vS  45  -oo 


^  Rejt  olol  ^\-  I'eirce's  criterinu. 


332 


THE    EASTERN    OBLIQUE    ARC. 


7.    CAIM')    SMAIJ,,   MAINK. 

q}=  43°  46'-7.  A  =69°  5o'-S. 

Theodolite  No.  i  was  mounted  over  the  triangulation  station.  The  mark  was  about 
i^  miles  from  the  station,  no  other  particulars  given  in  the  record.  A  set  of  observa- 
tions consisted  generally  of  3  pointings  on  the  mark/telescope  direct,  3  pointings  on 
the  mark,  telescope  reversed,  5  observations  of  the  star  with  time  and  level  record. 
The  instrument  was  then  reversed  and  the  observations  were  repeated  in  reverse  order. 
One  division  of  level  =  o"'97.  Ob.servers,  A.  D.  Bache,  W.  P.  Trowbridge,  and  C.  O. 
Boutelle.      Probable  error  of  a  single  result  for  azimuth  rb  o""96. 

SnJiiiiiarv  of  iTSutts  for  a'jiuni//!  a/  Cape  Small,  Maine. 


.  UrsEe  Minoris  near  upper  ciilinination 


a  Ursie  Minoris  near  elongations. 


Date. 

Position. 

Mark 
E.of  N, 

J 

Date. 

1851. 

0     ' 

'/ 

n 

1851. 

Oct.  14 

I 

8  40 

15-66 

-0-44 

Oct.  16 

I.S 

I 

17 '03 

-I  -81 

'7 

16 

II 

13 '44 

+  1-78 

17 

17 

III 

15  ^SS 

-0-13 

iS 

20 

V 

14-66 

+0  -56 

20 

23 

IV 

Mean 

15 -17 

+  0-05 
■30 

8  40 

15-22  +  0' 

Elonga-      Posi- 
tion,        tion. 

Mark 
E.  of  N. 

A 

E 

I 

0      ' 

8  40 

12  -50 

-HI -94 

E 

II 

13  '36 

-Hi  -oS 

W 

III 

74-0: 

4-0-43 

K 

IV 

i6-iS 

-174 

E 

V 
Mean 

16  -17 

-173 

8  40 

14-44  +  0' 

■50 

0     /        // 

8  40  14 

•83 

+0 

■31 

iSS  40  15 

■\\± 

'.0"  -29 

33  21    II 

•63 

155   '9  03 

■51 

Mean  of  group.s 

Dittrnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Sabattus 

Azimuth  of  Sabattus 

S.    SABBATTUS,   MAINE. 

(p=44°  oS'  -6.  A=7o°  04^  -7. 

Theodolite  No.  i  was  mounted  over  the  triangulation  .station.  The  mark  was 
placed  on  the  gable  of  a  barn  about  3  miles  distant  from  the  station,  and  it  showed 
under  an  angle  of  depression  of  i  J^°. 

A  .set  of  observations  consisted  generally  of  3  pointings  on  the  mark  with  telescope 
direct,  3  pointings  on  same,  telescope  reversed;  5  pointings  on  the  star,  if  near  culmi- 
nation, but  3  pointings  onl}-  when  near  elongation,  with  time  and  level  records.  The 
instrument  was  then  reversed  and  the  ob.servations  repeated  in  reverse  order.  Value  of 
I  divi-sion  of  level  o"'97.  Observers,  A.  D.  Bache  and  G.  W.  Dean.  Probable  error  of 
a  single  result  for  azimuth  it  i"'oo. 

Suintiiayy  of  results  for  azivinth  at  Sabattus,  IMaine. 


a  Urste  Minoris  near  lower  culmination. 


I  Ursce  Minoris  near  upper  culmination. 


Date. 

Position. 

Mark 
E.  of  N. 

J 

Date. 

Position. 

Mark 
E.  of  N. 

Z/ 

1853- 
July     13 

V 

0    '        // 
0  06  24  89 

-1-0-39 

'S53 

July     13 

V 

0    /        // 
0  06  25  -S3 

// 

-I  -02 

14 

I 

26-07 

-0-79 

14 

I 

2379 

-Hi '02 

15 

II 

22  -75 

-H2-53 

22 

III 

27-40 

—  2-12 

Mean 

0  06  25-28 

Mean 

0  06  24  -81 

Diurii 

al  aberration 

+0-31 

Diurn 

al  aberration 

-Ho -31 

THE    ASTRONOMIC   MEASURES. 


333 


Suinniaiy  of  results  for  azimulh  at  Sabatius,  Maine — continued. 

a  Ursfc  MinoHs  near  caslcrii  elongation.  1007  T.  Y.  C.  near  western  elon({alion. 


Date. 

1853- 
July     22 


IV 

IV 

III 
11 


24 
25 
30 

Mean 

Diurnal  aberration 


Mark 

K.  of  N. 


o  06  25  '00 

23-18 

24 '15 
22 '46 

n  06  2-},  70 
+  0-31 


A 

Date. 

Position 

It 
-1-30 

i«53- 
July      24 

IV 

+  0'52 

25 

III 

-0'45 

+  I'24 

Mean 

Diurnal  aberration 


Mark 
K.  of  N. 


o  06  23  61 
23  44 


o  06  23-53 
+0-31 


—0-08 
+0-09 


ISIean  b}-  culminations 

Mean  by  elongation.s 

Mean  of  groups 

Azimuth  of  Mark 

Angle  between  Mark  and  Mount  Independence 

Azimuth  of  Mount  Inde])endence 


o  06  25-35=^0-46 
23  -93^=0  -24 
o  06  24  -64 
I  So  06  24  ■64=!=o  -29 
204  24  58  -87 
24  31   23-51 


9.  MOUNT  indk:pe:ndence,  m.\ine. 


'^=43°  45''6. 


A=7o°   19'- 


Theodolite  No.  i  was  mounted  over  the  triangtilation  station.  The  mark  was 
located  nearly  north  of  the  station  and  distant  about  3  miles.  A  .set  of  observations 
generally  consisted  of  2  or  3  pointings  on  the  mark  with  telescope  direct,  2  or  3  pointings 
on  same,  telescope  reversed,  5  observations  on  the  star  with  time  and  level  record;  the 
instrument  was  then  reversed  and  the  observations  repeated  in  reverse  order.  One 
divi.sion  of  level  =o"'97.  Observer:  A.  D.  Bache.  Probable  error  of  a  single  result  for 
azimuth  ±0" '65. 

Sioniiiaty  of  results  for  azimuth  at  Mount  Iiidependcnee,  Maine. 


a  Ursie  Miuoris  near  eastern 
elongation. 


a  Urs£e  Minoris  and  {  frsce  Minoris 
near  western  elongation. 


Date. 

Position.          ^^IW, 

/I 

Date. 

Position. 

Mark 
W  of  N. 

A 

1849. 
Sept.  19 

V 

0    '      " 
0  10  49-48 

—0  05 

IS49. 

Oct.      9 

VI 

0     '        " 
0  10  49-69 

-0-21 

20 

VI 

49-14 

+0-29 

1 1 

I 

48-60 

+0-SS 

21 

VII 

49  •32 

+0-11 

12 

11 

50 -85 

-■•37 

Oct.    12 

I 

50-10 

-0-67 

13 

VII 

.so -20 

-0-72 

13 

II 

47 '27 

+  2-16 

>4 

III 

49  '93 

-0-45 

14 

III 

50-46 

- 1  '03 

14 

IV 

48 -82 

+0-66 

IS 

IV 
Mean 

50-21 

-0-78 

y  -27 

15 

V 
Mean 

.,S-26 

+  1-22 

0  10  49'43± 

0    10  49  '4Si:0' 

-24 

0        / 

ff 

Mean 

of  groups 

0    10 

49-45 

Diurnal  aberration 

-0 

•51      " 

Azimuth  of  INIark 

179  49 

10 

•86±o'i7 

Angle 

between  Mark 

and  Agamenticus 

207  06 

37 

74 

Azimi 

th  of  Agamenti 

CllS 

26  55 

48 

■60 

334 


THE    EASTERN    OBLIQUE    ARC. 


lO.    MOUNT    PLP:aSANT,  MAINE. ^ 


<^=44°  oi'-6. 


A  =  70°  49' -4. 


Theodolite  No.  i  was  mounted  over  the  triangulation  station.  The  mark  was  placed 
nearly  in  line  with  Mount  Blue,  on  the  summit  of  the  next  ridge  and  about  i  mile  dis- 
tant from  the  station.  The  angle  between  the  mark  and  Mount  Blue  was  measured 
micrometrically  with  the  eye-piece  micrometer  of  the  theodolite.  The  angle  of  depres- 
sion of  the  wand  placed  over  the  mark  was  2^°.  A  set  of  observations  consisted  of  3 
pointings  on  the  mark  with  telescope  direct,  3  pointings  on  same,  telescope  re\-ersed, 
5  observations  of  the  star  with  time  and  level  record;  the  instrument  was  then  reversed 
and  similar  observations  were  made  with  their  order  rever.sed.  One  division  of  level  = 
o"-97.  Observers:  A.  D.  Bache,  C.  O.  Boutelle,  and  W.  P.  Trowbridge,  U.  S.  E. 
Probable  error  of  a  single  result  for  azimuth  ±0" '90. 


SiniiJiiary  of  resnlls  for  aziunith  at  ISFount  Pleasant,  Maini 


a  Ursje  Minoris  near  lower  culmination. 


Date. 

185 1. 
July     22 

Aug.      3 

8 
14 


Mark 
E.  of  N. 


25  59  i'^'  '30 
19-17 
1777 

21  '00 


+0-76 
—0  'ii 
+  1  '29 

-I  -94 


a  Urste  Minoris  near  upper  culmination. 


July 
Aus;. 


I'osition, 

\' 
V 
III 


Mark 
E.  of  N. 


25  59  17 '6,^ 
20 '64 
I9'fil 


+  1-66 

-I '35 
-o'32 


25  59  19  ■o6±o"'4S 


25  59  19 '29*0" '60 


Mean  of  groups 

Diurnal  abberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Mount  Blue 

Azimuth  of  Mount  Blue 


25  59  19-16. 
+0  •31. 
205  .59  19 '47^0'' -34. 

02  '09. 
2"5  59  2'  '56. 


II.    AG.AMENTICliS,    MAINE. 

<p=43°   i3''4.  A=7o°  4i'-6. 

Theodolite  No.  i  was  mounted  over  the  triangulation  .station.  The  mark  was  .situ- 
ated on  a  hill  abotit  2  miles  distant.  A  .set  of  okservations  consisted  of  3  pointings  on 
the  mark,  telescope  direct;  3  pointings  on  .same,  tele.scope  reversed;  5  pointings  on  .star 
with  time  and  level  records;  the  instrument  was  then  rever.sed  and  similar  observations 
were  made  in  the  reverse  order.  One  division  of  level  =o"'97*.  Observer:  A.  D.  Bache. 
Probable  error  of  a  .single  result  for  azimuth  =fci"'02. 


*  The  instrument  was  generally  kept  leveled. 


THE    ASTRONOMIC   MEASURES. 


335 


SininiKirv  al  rcsidh  for  a':i>UHlli  al  /\i^aiiii)ili(  us,  iMaiiw. 


a  Ursie  Miiioris  iif.'ir  cislcrii  eloiiHalioii. 


a  (rsu;  Miiiori-  near  western  eloiijialioii. 


Date 

I'ositioii. 

Mark 
I'.,  of  N. 

A 

Date. 

I'« 

^itioii 

Mark 
K.  of  N. 

J 

1S47. 
Sept.  17 

IV 

114  OS  59 '.S? 

-1   iri 

1847. 
Sept.  2i 

IV 

t  I  4    (>'5    60  -64 

-'"75 

22 

\' 

60-57 

-2 -16 

22 

\- 

58-12 

+0-77 

Oct.      4 

I 

57 '92 

+  0-49 

(Jet.      5 

1 

59  •'*3 

-0-94 

14 

II 

5S'3i 

+  0'I0 

15 

II 

58-18 

+0-71 

i6 

III 
Mean 

55  -feS 

+  2-7,5 
56 

17 

M 

III 
ean 

57-6*4 
114  OS  sS-89±o" 

+  1  -21 

1 14  oS  58  ■41+0" 

•38 

0 

/ 

// 

Mean  of 

groups 

I 

14 

08 

5S 

•65 

Diurnal 

aberration 

\  0 

•31         " 

Azimuth 

of  Mark 

294 

oS 

58-96-0-32 

Allele  between  Mark  and  Thon 

pson         291 

32 

"3 

■45 

A/.iniuth 

of  Thompson 

2 

36 

53 

•51 

12.    CUINSTOCK,    NI'-.W    H.\MI'.SHIKI-;. 


<P=43    3''  'o- 


=  71"  22'  2. 


Theodolite  No.  i  was  mounted  over  the  trian<i^ulation  station.  The  mark  was 
located  upon  the  highest  point  of  rock  on  the  summit  of  Mount  Belknap,  about  three - 
fourths  of  a  mile  from  the  station ;  light  was  shown  throtigh  a  three- fourths  inch  aperture, 
above  which  was  placed  \-erticall3'  a  wand  i  foot  high  and  i  inch  wide  for  day  obser\-a- 
tions.  A  set  of  observations  consisted  of  3  pointings  on  the  mark,  tele.scope  direct,  3 
pointings  on  same,  telescope  reversed,  5  pointings  on  the  star  if  Polaris,  or  6  if  6  or  24 
Ursae  Minoris,  with  time  and  level  record.  The  instrument  was  then  reversed  and  the 
observations  repeated  in  the  reverse  order.  Value  of  i  division  of  level  =i""oo. 
Observers,  G.  W.  Dean  and  R.  IC.  Halter.  Probable  error  of  a  single  result  for  azimuth 
±o"'82. 

Siiiinnaiy  of  irstills  for  atiinulh  at  (,'niislock,  .Wri-  Haiiif'.^/iirc. 


a  II  rs;e 

Min 

)ri> 

near  eastern  eloni. 

ation. 

5  rrs 

.e  Minoris  near  ni>i>er  enhnination 

Date.          I'ositio.i.           w'^'of  N. 

Zl 

Date. 

Position. 

Mark 
W.  of  N. 

J 

.  1S60. 

C        '            " 

" 

1S60. 

0     '       " 

>• 

July  24 

II 

40  29  49-54 

+0-36 

July    24* 

II 

40  29  51  -40 

-'•53 

25 

III 

50-66 

—  0-76 

2S* 

III 

52-90 

-3  03 

27 

III 

4S-23 

+  1-67 

27 

III 

49  01 

+0-S6 

28 

IV 

49-06 

+0-S4 

2S 

IV 

4S  63 

r 
+  1-24 

30 

I 

49  -6S 

+  0-22 

,30 

I 

48 -80 

+  1-07 

M 

II 

50-50 

-o-6o 

31 

II 

50  03 

--0-16 

Auk.  1 

\- 

49-94 

—  0  "04 

.\un.      1 

\- 

48  - 1 2 

+ 1  -75 

2 

IV 

51  -3"^ 

-1-4S 

2 

V 

49  4^ 

+0  39 

3 

I 

.so- 10 

-0-20 

0"  -21 

3 

Men 

1 
n 

50-48 

-0-61 

Mean 

40  -'u  49-901 

40  2i)  49  S7±o' 

'34 

Diurua 

1  aherr;\tiou            o-_^i 

Din 

nal  al>t 

rrati 

on           -0-33 

Mean  of 

group.s 

0 
40 

/ 
29 

49  '37       " 

Azimuth 

of  Mark 

'39 

3^' 

10-43  -o-iS 

Angl 

ebe 

twecn  Mark  ami  Mount 

rleasant 

7>^ 

13 

23    17 

Aziti 

uth 

of  Mount  Pleasant 

217 

43 

33  ^^^ 

►The  results  for  July  24  :uul  25  are  from  ohserv.Uions  of  24  l'rs;e  Minoris  and  of  6  l"rs;c  Minoris, 


< 


336 


THE   EASTERN    OBLIQUE   ARC. 


13.    UNKONOONUC,  NEW  HAMPSHIRE. 

<p=42°  59' -o.  A  =  7i°  35' -3. 

Theodolite  No.  i  was  mounted  over  the  triangulation  .station.  For  an  azimuth 
mark  a  lamp  with  reflector  was  set  up  at  Holt  station  about  34  miles  distant  from 
Unkonoonuc.  A  set  of  observations  generally  consisted  of  2  pointings  on  the  mark, 
telescope  direct,  2  pointings  on  same,  telescope  reversed,  5  pointings  on  the  star,  with 
time  and  level  record.  The  instrument  was  then  reversed  and  the  operations  repeated 
in  the  rever.se  order.  One  division  of  level  =  o"'96.  Ob.server,  A.  D.  Bache.  Probable 
error  of  a  single  result  for  azimuth  d=i"'64. 


Suiiniiary  of  results  for  aziniuni  at  Un/coiiooiiiic,  New  Hampshire 


a  tTrsse  Minoris  near  eastern 

elongation. 

" 

,  0,  and  i 

IlrsEC  Minoris  near 
elongation. 

western 

Date. 

Position. 

Mark 

E.  of  N. 

A 

Date 

I'osition 

* 

Mark 

E.  of  N. 

J 

184S. 
Sept.  28 

V 

0    /      " 
133  4S  14 '44 

-3 '27 

1S4S. 
Oct.  5 

IV 

» 

0      '      '/ 
133  48  II -84 

+0-63 

Oct.      5 

IV 

07-83 

+  3-34 

5 

III 

i 

08  '09 

+4-38 

.s 

ill 

I0'2I 

+0-96 

5 

III 

<! 

12  76 

-0-29 

6 

I 

13 'SO 

-2-33 

5 

IV 

a 

1301 

-0-54 

6 

II 

09  85 

+  1-32 

5 

V 

<i 

12-41 

+0-06 

6 

11 

^ 

13  '63 

-1    16 

6 

II 

tt 

i6'i7 

"3  70 

Mean 

82 

fi 

I 
Mean 

" 

11-87 

+0  -60 

133  48  II  'i-i±o" 

133  48  12-47  +  0" 

•53 

0 

// 

Mean  of 

groups 

13 

3     4<S 

II 

82 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Gunstock 

Azimuth  of  Gun.stock 


313     48     i2-i3±o-45 

117     12     5175 
196     35     20-38 


14.    THOMP.SON,    MASS.-VCHUSETTS. 


5=42°  36'-6. 


A  =  70°  43' -8. 


Theodolite  No.  i  was  mounted  over  the  triangulation  station.  The  mark  was  .situ- 
ated in  a  northerly  direction  on  a  high  rocky  bluff,  distant  from  the  station  about  one- 
third  of  a  mile.  Over  the  .small  opening  in  the  box  was  placed  a  wand,  a  half  inch 
wide,  for  day  observations.*  A  set  of  observations  generally  consisted  of  3  pointings  on 
the  mark,  telescope  direct,  3  pointings  on  same,  telescope  reversed,  5  pointings  on  the 
star,  with  time  and  level  t  records.  The  instrument  was  then  reversed  and  the  opera- 
tions were  repeated  in  the  reverse  order.  Chief  of  party,  A.  D.  Bache.  Probable  error 
of  a  single  result  for  azimuth  ±o"'84. 


*  T-wo  azimuth  marks  were  p\it  up;  the  results  were  referred  to  the  western  one  as  being  better  determined  than 
the  other;  the  angle  between  the  marks  was  4°  05'  o8"-99±o"-34. 
t  The  instrument  was  generally  kept  leveled. 


THE   ASTRONOMIC   MEASURES. 

SiunDiary  of  irs.Hlls  for  aziiHutli  at  'fhojiipsoii ,  Massachusetts. 


337 


o  Ursa;  Miiioris  near  eastern  elongation. 


o  Urs;e  Minoris  near  western  elongation. 


Date. 

Position.        ^^"^^^^ 

A 

Date. 

Position.         ..i^'fj'X,. 

A 

1846. 

0    /       // 

„ 

i.'<46. 

0   / 

,, 

Oct.  26 

1               2  02  39  76 

-0-44 

Nov.    5 

1 

2  02  41  73 

-084 

Nov.  .s 

1 1                       38 -06 

+  r26 

7 

II 

39  96 

-TO '93 

Dec.     1 

in                 4013 

-o-8i 
■43 

24 

III 
Mean 

40-98 

2  02  40  ■S9±o' 

— 009 

Mean             2  02  39'32±o' 

■35 

0 

/ 

// 

Mean  of  groups 

2 

02 

40' 10 

Diurnal  aberration 

0-31         // 

Azimuth  of  Mark 

177 

.S7 

20-2I±034 

Angle  between  Mark 

and  Manomet         i!S6 

35 

38'35 

Azimuth  of  Manomet 

35 

I 

21 

41-86 

15.    WACHUSETT,    MASSACHUSETTS. 


<p  =  42"  29'-3. 


A  =  7i°  53'-2. 


Theodolite  No.  i  was  mounted  over  the  triangtilation  station.  The  mark  was 
located  npon  the  highest  point  of  Little  Wachusett  Mountain,  about  i^  miles  distant; 
light  was  shown  throttgh  a  ^-inch  aperture,  and  day  observations  were  made  on  a  wand 
I  foot  high  and  i  inch  wide,  moimted  over  the  aperture.  A  set  of  observations  con- 
sisted of  3  pointings  on  the  mark,  tele.scope  direct,  3  pointings  on  same,  telescope 
reversed,  5  pointings  on  a  Ursae  Minoris  (or  6  on  A.  Ursae  Minoris)  with  time  and  level 
records.  The  instrument  was  then  reversed  and  similar  observations  were  made  in  the 
reverse  order.  Value  of  one  divi.sion  of  level  i""oo.  Observers,  G.  W.  Dean  and 
R.  E.  Halter.     Probable  error  of  a  single  result  for  azimuth  d::  o"'42. 

Suniinary  of  results  for  azimuth  at  Wachusett,  Massachusetts. 


a  Ursce  Minoris  near  eastern  elongation. 


A  Ursa;  Minoris  near  nppcr  culmination. 


Date. 

Position. 

Mark 
W.  of  N. 

A 

Date. 

rcsition. 

Mark 
W.  of  N. 

A 

iS6c. 

0 

/       // 

,, 

1S60. 

0    '       /' 

,, 

Sept.  26 

I 

174 

15  ^2-6^ 

-0-34 

Sept.  26 

I 

174  15  12 -oS 

+0-04 

2^ 

V 

u'95 

-t-0'34 

2S 

V 

12-S2 

-0-70 

2y 

IV 

1271 

-0-42 

29 

IV 

12-78 

-0-66 

30 

III 

I  2 '67 

-0-3S 

30 

III 

n-52 

+0-60 

Oct.      J 

II 

•3 '24 

-095 

Oct.      3 

II 

1211 

+0-01 

6 

IV 

12-13 

+  0-16 

6 

V 

II  "40 

+0-72 

7 

I 
II 

12-62 
II  -42 

+  0-S7 

0 

III 

11-27 

+  1  -02 

Mean 


174   15    I2-29±0"'15 


Mean 


174  15  i2-ij±o"-i7 


4192 — No.  7- 


Mean  of  groups 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Bald  Hill 

Azimuth  of  Bald  Hill 


174    15    12-21 

-0-31 
5  44  4S-io±o"-ii 

'-"^  32  53  "35 
24  17  41-45 


338 


THE    EASTERN    OBLIQUE    ARC. 


l6.    HARVARD   OBSERVATORY,    MASSACHCISETTS. 


<p  =  42°   22'-8. 


A  =  7i°  o-j''-]. 


Troughton  and  Simms  transit,  Coast  Survey  No.  5,  was  mounted  on  the  west 
transit  pier  of  Harvard  Observatory.  The  mark  was  a  bull's-eye  lantern,  showing 
through  a  hole  of  '4  inch  diameter  in  a  box  placed  on  a  trestle  21  feet  high  and 
strongl\-  1)raced.  Tlie  mark  was  found  to  be  about  7" "5  west  of  north,  and  was  on  the 
same  level  as  the  old  north  mark  for  the  east  transit.  The  aperture  appeared  at  an 
altitude  of  0°  6'  as  seen  from  the  west  transit.  A  board  2  by  2  feet,  painted  in 
alternate  stripes  of  black  and  white,  4  inches  wide,  served  for  day  mark.  Micrometric 
differences  were  measured  between  the  verticals  of  the  mark  and  star  as  it  passed  the 
meridian,  and  times  were  recorded  on  chronograph;  a  set  of  observations  generalh- 
consisted  of  10  pointings  on  the  mark,  clamp  west,  10  pointings,  clamp  east,  and  of  9 
transits  of  the  .star.  Levels  were  recorded.  One  division  of  level  =o"' 96;  the  value 
of  one  turn  (  100  divisions)  of  the  eyepiece  micrometer  was  found  to  be  =44" "81  from 
the  transits  themselves.  Observer,  A.  T.  Mosman.  Probable  error  of  a  single  result 
for  azimuth  zto"'4o. 


Summary  of  results  for  azimuth  at  Harvard  Observatory,  Massaehuseits. 


S  Ur,sse  Minoris 
at  lower  cul- 
mination. 


51  Cephei  at 
upper  culmi- 
nation. 


A  Ur.sjE  Minoris 
at  lower  cul- 
mination. 


Mark  West  of  North. 


Jan.  28 

Feb.    I 

7-60 

4 

4-63* 

5 

7-80 

7 

7.22 

13 

7 '57 

17 

7 '13 

19 

S-47 

25 

7 -83 

27 

2.S 

5-65 

Mar.     I 

6 '30 

9 

7-84 

II 

S-6i 

12 

7-92 

.Means  7  '50+0 

8-84 

7-85 

6-89 

8 -28 

7 '49 
7-29 

9 '01 

8 -80 
9-11 
7  92 
S-is 
7-i6 
7 '49 
7 '94 

8 -02  +  0"  '13 


7.47 

8-07 
7 '61 
8-02 
8-68 

7 '00 

8-20 
7 '30 


7  79±o"'>3 


Mean  of  (^  and  A  Urste  Minoris  at  upper  transit 

Mean  of  5 1  Cephei  at  lower  transit 

Mean 

Diurnal  aberration 


7-65 

8 -02 

7-84 

— o  '3 1 


Azimuth  of  Mark 

Angle  between  Mark  and  Blue  Hill 

Azimuth  of  Blue  Hill 

Difference  of  azimuths,  transit  and  dome 

Azimuth  center  of  dome  to  Blue  Hill 


179    59  52-47±o-i3 

176     23  05  -48 

356     22  57  -95 

+  2  28-42 

356     25  26  -4 


♦Rejected. 


_. 


THE   ASTRONOMIC    MEASURES. 


339 


17.    H1.UH    HII,I„   MAS.SACIllSKTTS. 


(^  =  42"    12' 


A  =  7i'^  06' '9. 


Theodolite  No.  i  was  niounled  over  tlie  triangulatiou  station.  A  set  of  observations 
consisted  of  3  pointings  on  the  mark,*  telescope  direct,  3  pointings  on  .same,  telescope 
reversed,  and  5  pointings  on  the  .star,  with  time  and  level  records.  The  instrument 
was  tlien  reversed  and  the  preceding  operations  repeated  in  the  reverse  order.  The 
instrument  was  kept  leveled.  Chief  of  party,  A.  D.  Bache.  Probable  error  of  a  single 
result  for  azimuth  d=o"'89. 


Suiiunary  of  rciulls  for  aziinutli  at  ISliic  Hill,  Alassacliusciis. 


a  Ursie  Minoris  near  western  elongation. 


o  frscK  Minoris  near  eastern  elongation. 


Date. 

Position. 

Mark 
K.  of  N 

J 

D.ite. 

I'osition. 

Mark 
E.  of  N. 

J 

1845.. 

0     '         'f 

,, 

1^45. 

0    1 

,1 

Sept.  24 

Ill 

2  02  33  7S 

-0'42 

Sept.  25 

Ill 

2  02  30-25 

+  262 

27 

IV 

33  75 

-o'.^9 

26 

IV 

33 -z" 

—0-41 

Oct.     I  rt 

VI 

34 '49 

-■■'3 

27 

IV 

33 '9' 

-1-04 

2 

I 

34 '59 

-1-23 

2S 

II 

33 '29 

-0-42 

3 

11 

30-99 

+  2 '37 

29 

V 

33 '32 

-0-45 

13 

v 

32 '57 

-1-0  79 

Oct.         I 

VI 

3'  '94 

+0-93 

Mean 

•.3S 

2 

I 
Mean 

34 '07 

o"-3 

-I  -20 

2  02  33 '36  ±0" 

2  02  32'S7± 

» 

0 

f 

// 

Mean  of  groups 

2 

02 

33"" 

Diurnal  aberration 

-0-31 

// 

Azimuth  of  Mark 

IS2 

02 

33 '42^0 

•25 

Angle  between  Mark  and  Manoniet 

'23 

54 

56  -63 

Azimuth  of  Manomet 

305 

57 

30-05 

18.    SHOOTFI.YING,  MASS.\CHfSETTS. 


<p=4i°  41' 


20'  -s. 


Theodolite  No.  i  was  mounted  over  the  triangulatiou  .station.  The  azimuth  mark 
was  distant  from  the  station  about  i  ^/i^  miles.  A  set  of  observations  consisted  of  3 
pointings  on  the  mark,  telescope  direct,  3  pointings  on  .same,  telescope  reversed,  and  5 
pointings  on  star,  with  time  and  level  records.  The  instriunent  was  then  reversed  and  the 
operations  repeated  in  the  rever.se  order.  Instrument  was  kept  leveled.  Chief  of  party, 
A.  D.  Bache.     Probable  error  of  a  single  result  for  azimuth  d=o"'86. 


*  No  particulars  given  in  record  respecting  the  a/imuth  mark. 


HO 


THE   EASTERN   OBLIQUE   ARC. 

Siiiiiinary  of  results  for  aziinulh  at  Shoot/lying,  Jfassac/nisetts. 


a.  UrsiE  ^ 

iiioris  near 

eastern  elongation. 

a 

Ursse  Minoris  near 

western  elOT 

gation. 

Date, 

Position. 

Mark 

E.  of  N. 

J 

Date 

Position. 

Mark 

K.  of  N. 

J 

184:,. 

0    '        " 

,, 

1845 

0     '        /' 

„ 

Aug.      1 

m 

49  oS  12  'IS 

+0  '52 

Aug. 

I 

Ill 

(9  08  15-13 

~i  '40 

4 

IV 

1  2  -QJ 

+0-64 

3 

IV 

1.5  '18 

-1-45 

5 

V 

ii-8S 

+079 

4 

V 

TI-lS 

+  2-55 

7 

I 

14-19 

- 1  '52 

7 

I 

13 '52 

+  0'2I 

8 

VI 

I2'l6 

+0  -51 

9 

VI 

13  01 

+  072 

12 

II 

13 'SI 

-0-84 

12 

II 

14  -35 

-0  '62 

13 

III 

Mean 

12 -So 

-0-I3 

'  '22 

Mean 

49  08  12  67  +  0' 

»9  08  13  73*0' 

'•42 

0       /         // 

Mean  of 

groups 

49  oS  13 

•20 

Diurnal  aberration 

+0 

•31 

// 

Azimuth  of  Mark 

2 

29  oS  13 

■51 

±0"24 

Angle  between  Mark  and  Manomet 

86  04  50 

77 

Azimuth 

of  Manomet 

I 

43  03  22 

■74 

19.    INDIAN,  MASSACHUSETTS. 

<p=4i°  25'7.  A  =  7o°  4o'7. 

Theodolite  No.  i  was  mounted  over  the  triaiigulation  station.  A  pole  at  Prospect 
Hill  served  for  a  day  mark,  but  .several  lights  were  used  for  reference  marks.  It  was 
found,  however,  that  the  day  and  night  observations  upon  the  Cape  Poge  Light,  the 
West  Chop  Light,  and  the  Tarpaulin  Cove  Light  were  discordant,  the  verticals  through 
the  centers  of  the  light-hou.ses  and  throtigh  their  focal  reflectors  not  being  coincident. 
A  set  of  observations  generally  consisted  of  several  pointings  on  one  or  more  of  the 
marks  with  telescope  direct  and  rever.sed,  and  6  pointings  on  the  star  with  time  and  level 
records.  The  instrument  was  then  reversed  and  the  operations  repeated  in  the  reverse 
order.  Instrument  was  kept  leveled.  Ob.servers:  A.  D.  Bache  and  C.  O.  Boutelle. 
Probable  error  of  a  single  result  for  a/imuth  zhi"'40. 

Sminnarv  of  rcsu/t'i  for  aciiiuit/i  at  Indian ,  Massachusetts. 


a  Ilrsa^  Minoris  near  western  elongation. 


a  ITrsje  Minoris  near  eastern  elongation. 


Date. 

Position. 

Ma 
W.  0 

rk 

f  N. 

A 

Date. 

1845- 

0 

, 

„ 

,, 

1S45. 

July    9 

VI 

140 

37 

36-62 

+3  '03 

July    10 

12 

I 

43  '03 

-3-38 

11 

13 

II 

41-90 

-2-25 

12 

14 

HI 

37  '78 

+  1-87 

13 

15 

IV 

40-25 

-0-60 

15 

16 

IV 

42-5,5 

-2-90 

17 

17 

V 

36-31 

+  3 '34 

18 

18 

VI 

38-78 

+  0-87 

Position. 

VI 

I 

I 
II 

III 
IV 
V 


Mark 
W.  of  N. 


140  37  41 -56 
40  68 
38-69 
37-98 
40  -08 
39-51 
40-94 


-I  -64 
-0-76 
+  1-23 
•f'  -94 
—0-16 
+  0-41 

—  I  -02 


140  37  39 -65  ±0" -64 


140  37  39 -92  ±0" -33 


Mean  of  groups 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Copecut 

Azimuth  of  Copecut 


140  37  3978 

-0-31 

39  22  20-53 

96  13  38-29 

335  35  58  '82 


10-36 


the:  astronomic  measures. 


341 


20.    COI'KCUT,   MASSAC HUSKTTS. 


<P=4i''   «'\V 


A  =71"  03' '6. 


Theodolite  No.  i  was  mounted  over  the  triangiilatiou  station.  A  small  tele.scope 
was  placed  a  few  feet  from  the  great  theodolite  to  .serve  as  collimator;  it  pro\-ed,  how- 
ever, to  be  ver\-  unsteady,  and  even  for  daj'  ob.servations  the  cross  threads  had  to  be 
artificially  illuminated.  For  the  ob.servations  near  the  eastern  elongation  eyepiece  C 
was  attached  to  the  theodolite;*  value  of  one  divi.sion  of  its  micrometer  =  o"'54.  Tiie 
station  Blue  Hill  was  used  for  a  day  mark.  A  .set  of  observations  of  Polaris  near  ea.stern 
elongation  generall}'  consisted  of  one  dozen  micrometric  obser\-ations  between  mark  and 
star,  telescope  direct,  and  the  same  number  with  telescope  reversed;  also  5  circle  read- 
ings on  collimator,  in.strument  direct,  and  5  readings,  instrument  reversed.  In  connec- 
tion with  the  observations  near  western  elongation  the  star  was  pointed  at  a  number  of 
times,  with  instrument  direct  and  reversed;  times  and  levels  were  recorded.  The  instru- 
ment was  kept  leveled.  Ob.server:  A.  D.  Bache.  Probable  error  of  a  single  result  for 
azimuth  ±i"'i5. 


Summary  of  results  for  azi 111 II III  al  Copcciil,  flfassaiiinsclts. 


a  Ursse  Minoris  iie.nr  eastern  elongation. 
Date.         Position 


Mark 

W.  of  N. 


I'rsiu  Mitiori.-.  near  \vi;slcrn  • 


Date. 


Position. 


Mark 
\V.  of  N 


'lonijatioii. 
J 


Sept.  24 

Oct.      I 

2 
4 
5 
8 


in 

IV 

\' 
\- 
\- 

V 

v 
v 


•1  42  5>  '4' 
.S2  '0,; 
5274 
.S3 '20 
54 '26 
53  '05 
5"  '95 
52 '29 

.)  .12  52 -62  J 


+  1  '21 

+0'59 

—  0'12 

-o-.sS 

-I  ■64 

-0-43 
+0-67 
+  o'.33 
■21 


Sept.  26 
27 

29 

Oct.       I 


III 
IV 

v 
v 
v 

V 


4  42  56 'Rl 
55 '19 
56  55 
52-86 
55  "04 
53 -S? 


—  I  ■7^ 
-013 
-I  49 
-h2-20 

4-1     IQ 


4  42  55 '06+0" -42 


Mean  of  groups 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  INIark  and  Rlue  Hill 

Azimuth  of  Blue  Hill 


4  42  53  "84 

— o  -3 1         // 
175   17  "6-5     rbo-3i 

O  ■QC) 
175     17    (16  -5 


2  1.    KKACONPOI-K,   RHODK    ISI-.VNI), 


<P  =  4I      59 


A  =  7i^ 


Theodolite  No.  i  was  mounted  over  the  triangulation  station.  Observations  were 
made  in  .sets  consisting  generally  of  3  to  6  pointings  on  the  mark  and  on  the  star,  with 
telescope  direct,  and  the  same  number  of  pointings  with  telescope  reversed;  the  instru- 
ment was  kept  leveled.  Ob.server:  A.  D.  Bache.  Probable  error  of  a  single  result  for 
azimuth  ±o"'69. 


*Onc  turn  of  eyepiece  micrometer  equals  too  divisions. 


J. 


342 


THE    EASTERN    OBLIQUE    ARC. 


SiiiiiDiaiy  of  I't'snlts  for  azimuth  at  Bfucoiipolt-,  R/iodt'  Island. 


a  Ursse  Minoris  near  western  elongation 


Date. 

Position 

1SS4. 

Oct.     31 

I 

Nov.     1 

I 

s 

III 

10 

III 

16 

II 

iS 

11 

Mark 

E.  of  N. 


2  02  26  '23 
25 '91 
25  "47 
25 '46 
23-63 
24-51 

2  02  25  ■20  +  0"  '27 


J 

ti 

-  I  03 

-0'27 
—  0'26 

.  +  1-57 
+  0-69 


(I  I'rsie  Miiiori.s  near  eastern  elongation. 


1S44. 
Nov.     1 


I 

I 
III 
III 

II 

II 


Mark 

K.  of  N. 


2  02  25  "41 

25-96 

27 '34 

26-77 

26  -55 

26  -55 
2  02  26 -43  +  0" -18 


i-I-02 

ho -47 
-o  -91 
-0  -34 

-O  -12 

-0-12 


Mean  of  groups 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  ami  KUk-  Hill 

Azimuth  of  Blue  Hill 


2     02     25  '82 

+0-31       // 

1S2      02      26'13d=0'20 

46    52    51-11 

22S     55      17-24 


22.    SPKNCEK,   KHoni-;    ISIv.\Nn. 


<P=4i°  40'-?- 


A  =  7i°  29'-7. 


Theodolite  No.  i  was  mounted  over  the  triangulation  station.  Two  azimuth  marks 
were  used;  their  angular  difference  is  4°  04'  i2"-64=bo"'i8.  All  measures  were  reduced 
to  the  eastern  mark.  The  observations  were  made  in  irregular  sets  of  a  number,  a  dozen, 
more  or  less,  of  micrometric  measures  between  the  star  and  the  mark,  with  telescope 
direct  and  telescope  reversed.  The  value  of  one  division  of  the  eyepiece  micrometer 
was  o""57;  it  was  not  used  in  connection  with  western  elongation  of  Augtist  14.  One 
division  of  level  C  =  o"-96,  but  the  instrument  was  generally  kept  leveled.*  Observer, 
A.  D.  Bache.      Probable  error  of  a  single  result  for  azimuth  d=i"-2s. 


Siiinuiaiy  of  irsittts  for  aziiniitli  at  Spencrr,  khodt'  Island. 


a  Ursit'  Minoris  near  eastern 
elongation. 


Aug.   13 

14 
15 
16 

17 


ljrs;e  Minoris  near  western 
elongation. 


Mark 
E.  of  N. 

J 

Date. 

Mark 
K.  of  N. 

A 

0       '          II 

1, 

1S44. 

0 

II 

II 

2    02    00  -95 

+  1  -95 

Aug.    14 

2 

02     04  '59 

-2-73 

02  -67 

-1-0  -23 

1.S 

02     01  -50 

+0  -36 

04-34 

-1-44 

16 

01     59-48 

-f2-38 

04  "02 

—  1-12 

04  -26 

-1-36 

01  -17 

+  1-73 
-43 

Mean 

n   2     02     02-90^0" 

2 

02     01  -86+1 

'  -01 

Mean  of  groups 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  bet-ween  Mark  and  Beaconpole 

Azimuth  of  Beaconpole 


2     02     02  -38 

+0-31       // 
1S2     02     02 -69^0 -42 
356     04     29  -67 
i«5     57     33  "02 


■  On  August  17  and  21  the  .star  -was  observed  direct  and  reflected. 


THE    ASTRONOMIC    MEASURES. 


343 


23.    MOUNT    T<JM,    MASSACHISKTTS. 

<p=42°    14' -5.  A  =  72°   ,V'<''9- 

Theodolite  No.  i  was  mounted  over  the  trian^iilation  station.  The  mark  was  located 
near  the  Pro.spect  Hou.se  on  Mount  Holyoke;  a  lij^ht  was  sliown  thnnigh  a  three-fourths- 
inch  aperture  in  the  box;  a  wand  al)Ove  the  opening  was  used  in  daytime.  A  set  of 
ob.servations  consisted  of  3  pointings  on  the  mark,  telescope  direct,  3  pointings  on  .same, 
telescope  reversed,  5  pointings  on  a  Ursae  Minoris  (6  in  the  case  of  6  Ursa;  Minorisj, 
with  time  and  level  records.  The  instrument  was  then  reversed  and  a  series  of  like 
ob.servations  was  made  in  the  reverse  order.  One  division  of  level  =i"'C)0.  Ob.servers, 
G.  W.  Dean  and  R.  E.  Halter.      Probable  error  of  a  single  result  for  azimuth  ±o"'j-j. 

SiDinnaiy  of  ic^nlt^  for  a^iuiuth  at  J/oiiii/  Tom,  Massachusetts. 


a.  Ursie  Minoris  near  eastern  elongation. 


Date. 

I'osition 

1S62. 

Jnly    27 

1 

JO 

II 

Aug.     I 

I 

,^ 

III 

■t 

IV 

7 

v 

S 

v 

10 

IV 

Mark 

K.  of  N. 


37  22  35-20 

33 'gs 

33 'Si 
35  '59 
34  "30 

32 '22 
32-15 

34  '09 


h  Ursic  Minoris  near  iii)ptr  enlniinn 
Date.         I'osition. 


Mark 
K.  of  N. 


,,  1S62. 

-  I  '28  Jnly    27 

-  0  '06  30 
4-o'ii  .'Vng.     I 


- 1  -67 
-0-38 
+  1  '70 
+  ■•77 
-0-17 


I 

II 
II 
III 
IV 
V 
III 


37  22  36  74 
34  '39 
34  62 
34  '92 
33  93 
3416 
34 '01 


—  2  06 

4-0'29 

to'o6 

-  o'24 

+  0'75 
+0-52 
+0-67 


37  22  33 -92  +  0" -29 


37  22  34-6S±o"-25 


Dinrnal  aberration  +0'3I 


Diurnal  aberration 


-0'33 


]Mfan  of  grotip.s  37  22  34  '62        // 

.\/.imuth  of  jNIark  217  22  34 -62^=0 '20 

Angle  between  Mark  anil  Monadnook         4  45  I2"SS 

.Azimuth  of  Monadnock  212  37  2174 


24.    SANIIFORD,  CDNXKCTICIT. 

(P  =  41°  27'-7.  A  =72°  57'-<). 


Theodolite  No.  i  was  mounted  over  the  triangulation  station.  An  azimuth  mark 
was  placed  on  the  highest  hill  in  a  westerly  direction,  and  about  1J2  miles  from  the 
station.  The  aperture  was  three-fourths  of  an  inch  in  diameter,  and  a  wand  i  foot  high 
and  I  inch  wide  was  placed  vertically  over  it.  A  set  of  observations  consisted  of  3  joint- 
ings on  the  mark,  telescope  direct,  3  pointings  on  .same,  telescope  reversed,  5  jxiintings 
on  the  .star  if  Polaris,  6  if  A-  Ursct  Minoris,  with  time  and  level  records.  The  instrument 
was  then  reversed  and  the  observations  repeated  in  the  reverse  order.  One  division  of 
level  =i"'oo.  Ob.servers,  G.  W.  Dean  and  R.  K.  Halter.  Probable  error  of  a  .single 
result  for  azimuth  ±  i"'2o. 


344 


THE    EASTERN    OBLIOUE    ARC. 


Sutfuiia)-}'  of  results  for  azimuth  at  SaiiJ/ord,  Connecticut 


Ursfe  Miiioris  near  eastern  elongation 


A  ITrsit  Minoris  near  upper  cuhnination. 


Date. 

Position. 

Mark 
W.  of  N. 

J 

Date 

Position. 

Mark 
W.  of  N. 

A 

lSfi2. 

0      / 

// 

1 86  2 

0    /        " 

„ 

Sept.    9 

I 

SS  49  04  79 

-0-.S4 

Sept 

10 

I 

88  49  07 -lo 

-1-96 

10 

I 

05 '95 

—  I  -70 

21 

II 

06 -81 

-1-67 

II 

II 

07-83 

-3-58 

22 

III 

04-14 

+  1  -oo 

21 

II 

04-96 

-0-71 

2i 

IV 

05  "67 

-0  53 

22 

III 

02  -35 

+  1   90 

25 

V 

0379 

+  1-35 

23 

IV 

03  '24 

+  1  -01 

26 

IV 

06-03 

—0  -59 

25 

V 

03 '37 

+0-SS 

27 

II 

02  -43 

+2-71 

26 

V 

03  -5.^ 

+0-67 

27 

in 

Mean 

02 -iS 

+  2-07 

■41 

Mea 

1 

88  49  04 ■ 23  ±  0' 

88  49  05-14  +  0' 

■44 

Mean  of  groups 

0             r 

SS    49 

04 

•69 

Diurnal  aberration 

• 

0 

•31 

Aziniu 

th  of  Mark 

9 

I       lO 

55 

■62  ±0  -30 

Angle 

between  Mark  and  Ruland 

«5     20 

30 

"34 

Azimuth  of  Ruland 

5     50 

25 

•28 

25.    WEST    HILLS,  NEW    YORK. 

<?>=4o°4S'-S.  A  =  73°  25'-6. 

Theodolite  No.  i  was  mounted  nearly  over  the  triangulation  station.  The 
azimuth  mark  was  placed  near  the  station  Huntington,  4,1  kilometers  distant  from 
West  Hills  station.*  A  .set  of  observ^ations  consisted  of  3  pointings  on  the  mark, 
telescope  direct,  3  pointings  on  same,  telescope  reversed,  5  pointings  on  the  star,  if 
Polaris,  6  if  fJ  Ursae  Minoris,  with  time  and  level  records.  The  instrument  was  then 
reversed  and  similar  observations  were  made  with  their  order  reversed.  One  divi- 
sion of  level=i"'oo.  Observer,  G.  W.  Dean.  Probable  error  of  a  single  result  for 
azimuth  zfco"'57. 

Sumuiary  of  results  for  azimuth  at  West  Hitts,  Nezv  York. 


a  Urs:e  Minoris  near  eastern  elongation. 


5  Ursie  Minoris  near  upper  culmination. 


Date. 

Position 

Mark 
E.  of  N. 

// 

Date. 

Positio 

1. 

Mark 
E.  of  N. 

A 

1865. 

0    '       V 

,, 

1.865. 

0 

,      ,f 

,, 

Aug.    4 

v 

2  23  58-23 

+ 1  -00 

Aug.     4 

V 

2 

23  58-63 

-Ho -55 

8 

IV 

59  02 

+0-21 

8 

IV 

58  '55 

+  0-63 

9 

II 

60 -87 

—  I  -64 

9 

II 

58-72 

+0-46 

II 

I 

58-21 

+  1  -02 

u 

I 

5876 

-(-0-42 

12 

III 

60-61 

-1-38 

12 

III 

59  '68 

—0-50 

15 

v 

58  46 

-1-0 -77 

15 

IV 

60  "oo 

-0-82 

16 

II 

58-85 

+0  -38 

16 

I 

59 '94 

-076 

18 

III 

n 

59 '62 

-0-39 
■25 

Me 

m 

2 

Mea 

2  23  59-23  +  0" 

23  59-18  +  0" 

■I? 

Diu 

rnal  aberration          +0-31 

Dm 

rna 

I  abc 

rration 

-t-033 

Mean 

of  groups 

2 

23 

// 
59 '53 

Reduction  to  station 

+0 

•40 

// 

Azimuth  of  Mark 

If- 

2 

23 

59 

"93  ±0-15    : 

Angle 

between  Mark  and  Wooster 

7 

26 

21 

■61 

Azimuth  of  Wooster 

1" 

74 

57 

3«'32 

*Tlie  geodetic  station  was  found  to  be  0-47  of  an  inch  SW.  of  the  point  at  which  the  azimuth  observations  were 
made;  the  correction  to  the  azimuth  when  referred  to  the  geodetic  station  is  40" -40. 


THE   ASTRONOMIC   MEASURES. 


345 


26.    BKACON    llll.f,,   M'.W    JKRSKY. 

<p=4()°  22'  4.  A=74°    '3' 7- 

The  Trouf^hton  &  Siinins  transit,  Coast  .Survey  No.  5,  was  mounted  over  the 
station;  focal  length  of  telesajpe  r"'i7,  clear  aperture  70""",  magnifying  power  about 
80.  Value  of  one  division  of  eyepiece  micrometer  o"'44«o±o"'oooi  at  21'  C.  One 
division  of  level  o"'96;  pivot  inetpiality  -\-o'"oi'j  for  clamp  west.  The  mark  was  located 
about  8  miles  north  of  the  statical  and  light  was  shown  through  a  i-inch  aperture. 
In  connection  with  the  ob.servations  for  time  micron)etric  measures  between  the 
verticals  of  mark  and  .star  were  made  for  the  determination  of  a/.inuitli.  A  set  of 
observations  consisted  of  15  tran.sits  of  S  IJrsae  Minoris  and  an  equal  number  of  transits 
of  5  [  Cephei  over  the  micrometer  thread  .set  in  advance  to  a  whole  turn  Ijetween  o  and  14: 
the  mark  was  observed  10  times  with  clamp  ea.st  and  an  equal  nunil)er  of  times  with 
clamp  west;  the  level  was  generally  read  l)efore  and  after  each  set.  C)bser\-er.  G.  W. 
Dean.  Probable  error  of  a  single  result  for  azimuth  dzo"'8r  for  f>'  Urs^e  Minoris  and 
±o""67  for  51  Cephei. 

Suiiiniaiy  of  results  for  a::i)niitli  at  /Iracoii  Hill,  Xcw  Jersey. 


6  UrsiL'  Minoris  near  npper  cnlniination. 


51  Cuphei  iK-ar  lower  culmination. 


Date. 

C 

ani]). 

Mark 
W.  of  N. 

J 

Dale. 

Clanii). 

Mark 
W.  of  N. 

A 

1875. 

„ 

„ 

i«7.S. 

„ 

., 

Aug.  19 

E 

7 '95 

-o'S6 

Aug.   19 

E 

7-90 

-024 

21 

W 

5  -53 

+  1  '56 

21 

W 

6 -07 

+  1-59 

25 

W 

8-63 

-1-54 

25 

W 

S-7S 

—  I    12 

26 

E 

6-II 

+  0-98 

26 

E 

7  '21 

-045 

27 

W 

6 '50 

+0  -y) 

27 

\\ 

7  41 

+  0-25 

2S 

E 

7 '81 

-072 

28 

E 

s-5g 

-0'93 

Mean 
Diurnal  a 

berr 

■itiou 

7 '09  +  0" 
-0-33 

•33 

Mean 
Diurnal  a 

berration 

7-66-0" 
-030 

■27 

Mean  of  groups 

Azimuth  of  Mark 

Aiifilf  between  Mark  and  Weasel 

A/.iinttth  of  Weasel 


o 


7  '06 


•79     59     52  942=0 -21 

3     35     36  95 
I  S3     35     29  "^9 


27.    Mor.NT    KOSK,    Ni;\V    JICKSKV. 

<p=4o°  22'- 1.  A=74°  4;/-4. 

The  60""  direction  theodolite  No.  2  was  mounted  over  the  triangulation  station  and 
15  feet  above  the  ground.  The  mark  was  i"2o  kilometers  distant.  A  set  of  observa- 
tions consisted  of  3  pointings  on  the  mark,  telescope  direct,  3  pointings  on  the  same, 
telescope  reversed ,  and  5  pointings  on  the  star,  telescope  direct,  and  5  pointings  on  the 
same,  telescope  reversed,  with  time  and  level  records.  One  division  of  level  =i""2s. 
Observer,  J.  K.  Hilgard,  assisted  by  G.  W.  Stevens.  Probable  error  of  a  single  result 
for  azimuth  zhi"o7. 


546 


THE    EASTERN    OBLIQUE    ARC. 


S/n/n/iarv  of  results  for  aziunitli  at  Mount  I\osc\  Nciv  Jersey. 


:  UrsLt  Minori^  near  easterifelongation. 


a  UrsEe  Miiioris  near  western  elongation. 


Date. 

Position. 

Mark 

E.  of  N. 

J 

Date. 

Position. 

Mark 
E.  of  N. 

A 

1S52. 

0     '      " 

„ 

185 

2. 

0     /       f 

,, 

Aug.   13 

I 

75  5^  03  '4^ 

-0-72 

Aug. 

13 

I 

75  57  63  'SS 

-2-08 

14 

11 

03  '50 

-074 

14 

II 

59 '94 

+  1-36 

14 

II 

00  -78 

+  1-98 

15 

III 

61  -24 

+o-o6 

15 

III 

00-30 

+  2-46 

17 

V 

60-42 

+  0-SS 

16 

IV 

03-48 

-0-72 

19 

IV 

61  -50 

—  0'20 

iS 

V 

04  '33 

- 1  'S? 

19 

III 
Mean 

03  -42 

-0-66 
'■40 

Mean 

75  58  02-76  +  0 

75  58  01  -30±o 

'-40 

0 

/ 

/  f 

Mean  of  groups 

75 

S''^ 

02 '03 

E 

(iurnal  aberration 

rO-31        // 

A 

zinuith  of  Mark 

255 

5'S 

o2-34±o-3i 

A 

iigle  between  Mark  an 

1  Mount 

Holly 

1 1 1 

4,S 

53 '25 

A 

ziniuth  of  Mount  Holly 

7 

46 

55-59 

2.S.    V.\RD,    PENNSYIA'ANIA. 


<P=39    5- 


A  =  75^ 


The  60'''"  direction  theodolite  No.  2  was  mounted  over  the  triangulation  station. 
A  set  of  azimuth  observations  consisted  of  3  pointings  on  the  mark  and  3  pointings  on 
the  star,  with  telescope  direct,  and  the  .same  number  of  pointings  on  mark  and  star 
with  telescope  reversed.  Times  and  levels  were  recorded.  One  division  of  level  =0" '94. 
Observer,  J.  E.  Hilgard.     Probable  error  of  a  .single  result  for  azimuth  d=o"'99. 


Suiiiiuary  of  results  for  aziiiiut/i  at  }'ard,  Peuusyti'aiiia. 
a  Ursre  Minoris  at  various  hour  angles. 


Date. 

Po 

sitioi 

Mark 

E.  of  N. 

/] 

1S54. 

0 

/        // 

II 

Oct,    27 

v 

0 

7  3'  -87 

+  2-07 

Nov.     I 

IV 

34 '23 

-0-29 

I 

III 

36-89 

-  2  '95 

2 

I 

33-68 

+0-26 

2 

V 

34   15 

-021 

5 

III 

3272 

+  1-22 

5 

V 

34-37 

-0-43 

5 

IV 

32-26 

+  1-68 

5 

II 

35  -32 

-1-38 

6 

n 

I 

33  -94 

0-00 

Mea 

0 

7  33-94*0" 

■31 

Diu 

rnal 

aber 

ration 

+  0-31 

Azimuth  of  Mark 

Angle  between  Mark  and  Lippincott 

Aziunith  of  Lippincott 


I  So  17  34 -25^0 -31 
167  00  04  -32 
347   17  3«'57 


THE   ASTRONOMIC   MEASURES.  347 

29.    PRINCIPIO,    MAK\I.AND.* 

'P=39°  3.'5''5-  A  =76°  f)o'-3. 

The  60""  direction  theodolite  No.  2  was  mounted  over  tlie  trian<^nlatioii  station; 
the  mark  was  at  Carpenter's  Point,  about  t,'/j  miles  distant.  A  single  result  for 
azimuth  is  derived  from  19  .sets,  each  consistinj^  of:  3  pointings  ou  the  mark,  reversal 
of  instrument;  3  pointing  on  the  mark,  4  to  (■>  pointings  on  the  star,  followed  by  the 
same  operations  in  the  reverse  order,  with  tlie  necessary  noting  of  time  and  level 
readings;  circle  used  in  V  positions.  Ob.server,  R.  D.  Cntts.  Probal^le  error  of  a  single 
result  zb  I  "75. 

Results  for  azimuth  from  observations  of  a  i'rs(r  Miiions  near  eastern  eloui^ation,  in  August  and 

Septemlwr,  1866. 

o        /  // 

Mark  west  of  .south  3  05  07  '20 
Diurnal  aberration  — o  -32 

Azimuth  of  Mark  3  05  07  •52^=0'''  "40 

Angle  between  Mark  ami  Turkey  Point  i   30  24  'oi 

Azimuth  of  Turkey  Point  1    34  43  51 

30.    CAPK   HENLOPEN    LICHT-HOISE,    DELAWARE. 

<p=3.S°46'7.  A  =  75°o5'-r. 

The  30""  direction  theodolite  No.  135  was  mounted  over  the  eccentric  geodetic 
station,  about  15  meters  north  of  the  center  of  the  Light-House;  the  mark  was  ai 
Brandy  wine  Shoal  Light-Hou.se.  A  single  result  for  azimuth  is  derived  from  49  .sets, 
each  consisting  of  a  pointing  on  the  mark,  a  pointing  on  the  .star,  reversal  of  instrument 
and  pointings  on  star  and  mark,  noting  of  times  and  level  readings.  Circle  used  in 
XVn  po.sitions.  Ob.server,  O.  B.  French.  Probable  e-ror  of  a  single  re.sult  =t  \"~b 
for  a  Unsse  Minoris  and  dzo"'97  for  A  Ur.sae  Minoris. 

Results  for  aziiiudh  from  observations  of  ix  t'rs<e  Jfinor/s  and  X  Urstr  Minoris  at  various  hour 

angles,  in  Seftemt'er,  /Sgy. 

o        /  //  // 

Mark  W.  of  N.,  28  results  from  observation.^,  of  it  I'rsLu  Minoris  6  14  23  ■2i=:0"33 

Mark  W.  of  N.,  21  results  from  ob.servations  of  ,\  Trsa'  Minoris  22  ■i9=rO'2i 

Weighted  mean  according  to  the  probable  errors  22  "481^0  "iS 

Indiscriminate  mean  of  49  sets  22  77 

Mean  value  adopted  22  "62 

Diurnal  aberration  o  -32 

Azimuth  of  Mark  173  45  37  -70— 021 

Reduction  to  center  of  Cape  Henlopen  Light- House  —20  -37 
Azimuth,  Cape  Henlopen  Light-Hou.se  to  Brandywine  Shoal  Light-House         173  45   17  "33 


♦For  the  complete  al)stract  and  coinbiiiation  of  results  for  azimuth  at  this  and  the  succeeding  ij  stations,  all  of 
which  are  common  to  the  .\rc  of  the  ,w'h  Parallel  and  the  Oblique  .\rc,  see  "The  Transcontinental  Triaug\ilalion  " 
U.  S.  Coast  and  Geodetic  Survey,  Special  Publicatiou  No.  4,  Washington,  D.  C,  1900. 


348  THE    EASTERN    OBLIQUE    ARC. 

31.    MARRIOTT,    MARVi:,ANr). 

</;=3S°  52'-4.  A=76°  36'-6. 

The  60""  direction  theodolite  No.  2  was  mounted  over  the  triangulation  station. 
A  .single  result  for  a/.inuith  is  derived  from  a  set  of  observations  con.sisting  of  al)out 
one  dozen  pointings  on  the  .star,  one  half  with  telescope  direct  and  one- half  with  tele- 
scope reversed,  and  corresponding  pointings  on  the  mark,  with  noting  of  times  and  level 
readings.  Circle  used  in  XI  po.sitions.  Observers:  A.  D.  Bache,  J.  Hewston,  jr.,  and 
G.  Davidson.      Probable  error  of  a  single  result  ±i"'92. 

/\'t'S!(//s  for  aziuiulh  from  obscr-'ations  of  a,  6,  and  A   I'rscc  Minoris  near  eastern  elongation  and  of 
a,  li,  0,  a)id  l  Urscc  Minoris  and  of  a  Urscc  Majoris  near  ivestern  elongation,  June,  iS4g. 

o        /  //  // 

Mark  W.  of  X.,  from  8  star.s  near  t:a.stern  elongation  o  58  27  •38zto '68 

Mark  \V.  of  N.,  from  8  stars  near  western  elongation  28  '561^071 

Mean,  Mark  west  of  north  27  '97 

Diurnal  aberration  -o"3i 

Azininth  of  Mark  179  01  32  '34^=0  '48 

Angle  between  Mark  and  Hill  82  23  48  "98 

Azimuth  of  Hill  96  37  43  '36 

32.  WEBB,    MARYL.AND. 

'?'=39°  o5'-4.  A=76°  4o"5- 

The  75""  direction  theodolite  No.  i  was  mounted  over  the  triangulation  station. 
The  mark  was  about  i  mile  distant.  A  single  result  for  azimuth  is  derived  from  a  set 
of  observations  consisting  of  6  pointings  on  the  mark,  one-half  of  which  with  telescope 
direct  and  the  other  half  with  tele.scope  reversed;  12  pointings  on  the  star,  one-half 
with  telescope  direct  and  one-half  with  telescope  rever.sed;  finally  6  more  pointings 
on  the  mark  as  before,  noting  time  and  level  readings.  Circle  u.sed  in  V  positions. 
Observers,  A.  D.  Bache  and  G.  \^^.  Dean.     Probable  error  of  a  single  result  ±o"'67. 

Results  for  azimuth  from  observations  of  a  IJrscr  Minoris  near  eastern  and  icestern  elongations,  in 

October  and  A'oz'ember,  fS§o. 

o  /  //  // 

Mark  E.  of  N.  a  Ursae  Minoris,  5  sets  near  eastern  elongation 

Mark  E.  of  N.  a  ITrsie  Minoris,  5  sets  near  western  elongation 

Mean,  ]Mark  east  of  north 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Soper 

Azimuth  of  Soper 

33.  HILI,,    MARYLAND. 

'P=38°  53'-9-  A  =  76°  52'-8. 

The  75  ""  direction  theodolite  No.  i  was  mounted  over  the  triangulation  station. 
Mark  in  line  to  station  Webb.  A  single  result  for  azinuith  is  derived  from  13  .sets  of 
oUservations,  each  con.sisting  of  6  pointings  on  the  mark,  half  with  telescope  direct  and 
half  with  tele.scope  rever.sed;  10  pointings  on  the  star,  half  with  telescope  direct  and 
half  with  telescope  reversed,  and  finally  6  pointings  on  the  mark  as  before,  with  noting 
of  times  and  level  readings.  Circle  u.sed  in  V  po.sitions.  Ob.servers,  A.  D.  Bache  and 
G.  W.  Dean.      Probable  error  of  a  single  result  ±o"'83. 


6 

07 

45  •42iirO-28 

45  •69=bo  -35 

6 

07 

45 '56 
-h-o-32 

186 

07 

45-88±o-2r 

97 

07 

56  64 

88 

59 

49-24 

39    46 

56 -83 -o  42 

57  T?^" '3' 

6i  o;     Xot  used 

57  30 

+0-32 

219     46 

57  •62^=0-26 

(x> '27 

219     46 

57  ••S9 

THE   ASTRONOMIC    MHASlKi:S.  349 

Remits  for  aziniuth  from  observations  of  a  IJrsec  Miiioris  near  eastern  and  'luestcrn  elongations  and  of 
A  (Jrsie  Minoris  near  upper  culmination ,  in  Septonljer  and  October,  /8§o. 

o  /  //  // 

Mark  E.  of  N.,  5  results  from  <r  llrsie  Minoris  near  eastern  elongation 

Mark  E.  of  N.,  5  results  from  <r  Ursa.-  Minoris  near  western  elongation 

Mark  E.  of  N.,  3  results  from  X  Ursa.'  Minoris  near  uijjjer  culmination 

Mean,  Mark  east  of  north 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Webb 

A/.inuith  of  Webb 

34.    SOPER,   MARYLAND. 

<P=39°  05' -2.  A  =76°  57' -o. 

The  75"™  direction  theodolite  No.  i  was  mounted  over  the  trianj^ulation  station, 
the  mark  being  to  the  sotithward,  distant  442  meters.  A  single  result  for  azimutli  is 
derived  from  10  sets  of  observations,  each  consisting  of  6  pointings  on  the  mark,  10 
pointings  on  the  star,  one-half  with  telescope  direct  and  half  with  telescope  reversed,  6 
pointings  on  the  mark,  with  noting  of  times  and  level  leadings.  In  case  of  ctilminations 
the  above  operations  were  repeated.  Circle  used  in  V  positions.  Observer,  A.  D.  Bache. 
Probable  error  of  a  single  result  zbo""92. 

Result  for  azimuth  frotn  observations  of  a  Urscc  Minoris  near  loivcr  culmination,  A  Urser  Minoris 
near  eastern  elongation,  and  fi  Ursee  Minoris  near  ivestern  elongation,  in  fuly,  /S^o. 

o  /  // 

Mark  east  of  north,  indiscriminate  mean 

Diurnal  aberration 

Azinuith  of  Mark 

Angle  between  Mark  and  Webb 

Azimutli  of  Webb 

35.    SE.\TON,    ni.STRlCT   OK    COI.rMKIA. 

<P=2>'^°  53' ■4-  A  =77°  00' -o. 

The  75""  direction  theodolite  No.  i  was  mounted  over  the  triangulation  station, 
and  the  mark  was  on  the  tower  of  the  Soldiers'  Home,  about  3/2  miles  distant.  A 
single  result  for  azimuth  is  derived  from  34  sets,  each  set  of  observations  consisting 
of  8  pointings  on  the  mark  and  8  pointings  on  the  .star,  one-half  with  telescope  direct 
and  one-half  in  reversed  position.  The  star  was  observed  alternately  direct  and 
reflected  in  mercury,  times  noted.  The  circle  was  used  in  \'II  po.sitions.  Observer, 
C.  O.  Boutelle.      Probaiile  error  of  a  single  result  ±o"'72. 

Result  for  azimutli  from  observations  of  a  t'rsic  Minoris  at  various  hour  angles,  in  December.  /S6S. 

and  fanuary,  iSb^. 

o  /  // 

Mark  west  of  north  10  01  13  73 

Diurnal  aberration  o  "32      /' 

Azimuth  of  Mark  169  5S  46  ■59=^:0  mS 

Angle  between  ;Mark  and  Hill  95  34  07-17 

Azimuth  of  Hill  265  32  53  76 


17S 

'9 

3,S  -22 
'fO'32          // 

35S 

19 

3S  •54=^0  '29 

89 

3" 

15-08 

26S 

49 

23-46 

3" 

52 

60  •62±o  '51 
59-29±o-48 
59  "955 
+0-315 

2IO 

53 

00  -27^=0  '37 

O 

0[ 

41  '5^ 

2IO 

54 

41  -7^ 

350  THE    EASTERN    OBLIQUE    ARC. 

36.    CAl'STEN,   DISTRICT   OK    COLUMBIA. 

'P=38°55'-5.  A=77°o4'-4. 

The  75""  direction  theodolite  No.  i  was  mounted  over  the  triangulation  station,  and 
the  mark  was  about  a  quarter  of  a  mile  distant.  A  single  result  for  azinuith  is  derived 
from  a  set  of  observations  consisting  of  6  pointings  on  the  mark,  one-half  with  telescope 
direct  and  one-half  with  telescope  reversed,  10  pointings  on  the  star,  one-half  with  tele- 
scope direct,  and  one-half,  telescope  reversed;  finally,  6  more  pointings  on  the  mark 
with  times  noted  and  levels  read.  For  culminations  two  sets  were  taken  and  coupled, 
one  made  before,  the  other  after  culmination.  Circle  used  in  V  positions.  Observer, 
G.  W.  Dean.  Probable  error  of  a  single  result,  star  near  elongation  dLo"'88  and  star 
near  culmination  =ti"'o8. 

A'cs/iZ/s  /'or  aziinutlt  from  observations  of  a  Urscc  Jfinoris  near  easier)!  e/om^a/ion  and  near  Imvcr 

enhninafion ,  in  May  and  June,  iS^i. 

o  /  //  // 

Mark  E.  of  N.,  3  observations  near  eastern  elongation 

Mark  E.  of  N.,  5  observations  near  lower  culmination 

Mean,  Mark  east  of  north 

Diurnal  aberration 

Azimuth  of  Mark  ♦ 

Angle  between  Mark  and  vSoper 

Azimuth  of  Soper 

37.    SUG.\R    LOAF,    MARYLAND. 

<p  =  39°  i5'-8.  A  =77°  23'-6. 

The  50'"  direction  theodolite  No.  113  was  mounted  over  the  triangulation  station, 
and  the  mark  was  near  the  railroad  station  at  Barnsville  t^'^  miles  distant.  Thirtv- 
three  sets  of  observations  were  made,  each  consisting  of  a  pointing  on  the  mark,  2 
pointings  on  the  star,  one  direct,  the  other  reflected  in  mercury,  reversal  of  instrument, 
observations  as  before,  but  in  reversed  order,  times  noted.  The  circle  was  used  in  XI 
positions.  Observers,  C.  O.  Boutelle  and  F.  D.  Granger.  Probable  error  of  a  single 
result  it  I "'02. 

Result  for  azimiitk  from  observations  of  a  Urscc  IMinoris  at  various  hour  angles,  in  October  and 

Noveinber,  iSjg. 

o  /  // 

Azimuth  of  Mark,  east  of  north 

Diurnal  aberration 

Azinuith  of  Mark 

Angle  between  Mark  and  Bull  Run 

Azimuth  of  Bull  Run 

38.    MARYLAND    HEIGHTS,    MARYL.^ND. 

9)  =  39°  2o'-5.  A  =  77°  43'-o. 

The  ys*""  direction  theodolite  No.  i  was  mounted  over  the  triangulation  station; 
the  mark  was  on  a  hill  back  of  Knoxville  di.stant  about  3^  miles.  Thirt\'-five  sets 
of  observations  were  taken,  each  set  consisting  of  a  pointing  on  the  mark,  2  pointings 
on  the  star,  one  direct,  the  other  reflected  in  mercury,  reversal  of  instrument  and  series 
of  observations,  as  before,  but  in  the  reverse  order,  times  noted.  The  circle  was  used 
in  V  positions.  Observers,  C.  O.  Boutelle  and  F.  D.  Granger.  Probable  error  of  a  set 
or  .single  result  ±  i"'io. 


67 

01 

59  "96 

+0  -32     // 

47 

01 

60  -28=^0  '20 

45 

27 

[6-51 

32 

29 

16-79 

'J'lIK    ASTRONOMIC    MEASURES.  35 1 

Rcsnil  for  a::ii)iulh  from  o/ysi-rva/iotis  of  <t  I'rscr  Miiioris  at  I'arious  lioiir  auf^les,  in  October,  iSyu. 

o  /  // 

Mark  cast  of  lu^rth  loS  14  43 '46 

Diurnal  aberration  •  o  '32      // 

Azimuth  of  Mark  2SS  14  43  78nro-i8 

Angle  between  Mark  and  Bull  Kun  70  28  23  to 

Azimuth  of  Bull  Run  358  43  06  "88 

39,    liiT.r,  Ktix,  \TRc;iNrA. 

(^=38°   52'-<,.  -1    -77°   42' -2. 

The  75""  direction  theodolite  No.  i  was  mounted  (jver  tlie  tnunsfulation  station;  the 
mark  was  on  Hi^h  Point  Mountain  abcnit  i  )-j  miles  distant.  Thirt_\-five  sets  for  azinmtli 
were  taken,  each  consi,stin<(  of  a  pointing  on  the  mark,  2  p()intin<(s  on  the  star,  first 
direct,  .second  reflected  in  mercury,  reversal  of  instrument  and  series  of  similar  observa- 
tions in  the  rever.se  order,  times  noted.  Circle  n.sed  in  \'II  positions.  Observer.  C.  O. 
Botttelle.      Probable  error  of  a  .set  or  .single  result  ±i"'20. 

Result  for  aziiiiiit/i  from  ol^scrvalioiis  of  a   Uracc  Minoris  at  various  hour  atij^tcs.  in   October  and 

November,  /Sj/. 

o  /  // 

Mark  west  of  north  158     36     29  -98 

Diurnal  aberration  0*32       " 

Azimuth  of  Mark 

Angle  between  Mark  and  Peach  Grove 

Azimuth  of  Peach  Grove 

40.    CI,.VRK,  VIRr,INl.\. 

q)=2,H°    18' 7.  A  =  7S°oo'-2. 

The  75""  direction  theodolite  No.  i  was  moinited  over  tlie  triangulation  station; 
mark  at  Rapidan  railroad  .station,  nearly  5 '54  kilometers  distant.  Thirty-five  sets  of 
observations  were  taken,  each  set  consi.sting  of  a  pointing  on  the  mark.  2  pointings  on 
the  star,  one  direct,  the  other  reflected  in  mercury,  reversal  of  in.striunent  and  series  of 
observations,  as  before,  but  in  the  reverse  order,  times  noted.  The  circle  was  n.sed  in  \' 
positions.      Observer,  C.  O.  Boutelle.      Probable  error  of  a  single  .set  or  result zb  i"  "09. 

Result  for  aziinulli  from  observalious  of  a  I'rscc  Minoris  at  various  hour  angles,  in  August,  iSji. 

Of  f 

Mark  west  of  north  85  30  59  -64 

Diurnal  aberration  0-32      " 

Azimuth  of  Mark  94  29  00 '68^0 'iS 

Angle  between  Mark  and  Bull  Run  107  50  27  "09 

Azimuth  of  Bull  Run  202  19  27  77 

41.     I.OXC.    RU)rNTAIN,    \  IKOINI.X. 

H>=},1°   17'  S-  A  =  79°  05' -2. 

The  35""  direction  theodolite  No.  lo  wa.s  mounted  over  the  triangulation  station; 
the  mark  was  on  belfry  of  court-house  at  Lynchburg,  abotit  10  miles  distant.  Fort>- 
six  sets  of  observations  were  made,  each  set  ctinsisting  of  a  pointing  on  the  mark,  2 
pointings  on  the  star,  one  direct,  the  other  reflected  in  mercury,  reversal  of  in.stntment 
and  series  of  observations,  as  before,  but  in  the  reverse  order,  times  noted.     The  circle 


21 

23 

30-34 

242 

29 

57 -Si 

263 

53 

28-15 

352  THE    EASTERN    OBLIQUE    ARC. 

was  used  in  XXIII  positions.     Observer,  A.  T.  Mosman.     Probable  error  of  a  set  or  of 
a  single  result  ±i"'54. 

Remit  for  azifuuth  from  ohseri^ations  of  ix  Ihscr  Minoris  at  various  hour  ambles,  in  November,  1875. 

o  /  // 

Mark  west  of  north  20  48  1 3  '  1 1 

Diurnal  aberration  — o  '32       " 

Azimuth  of  Mark  159  u  47 -21^0 -23 

Angle  between  ]Mark  and  Spear  64  16  54  '53 

Azimuth  of  vSpear  223  28  41  74 

42.  KI,I,IOTT    KNOB,    VIRGINIA. 

(^=38°   10' -o  A=79°   18' -9 

The  50"'  direction  theodolite  No.  114  was  mounted  over  the  triangulation  station, 
and  the  collimator  was  mounted  on  a  brick  pier  29  feet  distant.  Thirty  sets  of  observa- 
tions were  made,  each  set  consisting  of  a  pointing  on  collimator,  2  pointings  on  the  star, 
one  direct,  the  other  reflected  in  mercury,  times  noted,  reversal  of  instrument  and  series 
of  observations,  as  before,  but  in  the  reverse  order.  The  circle  was  u.sed  in  X  positions. 
Observer,  A.  T.  Mosman.      Probable  error  of  a  single  re.sult  ±i"'50. 

Result  for  aziinutli  from  oliservations  of  ^x  IJrscr  iMinoris  at  I'arious  hoiiiauiilcs.  in  .liiffust.  jSyS. 

o  /  // 

Collimator  east  of  north  i  41  34  '52 

Diurnal  aberration  ^o  '32       " 

Azimuth  of  Collimator  181  41  34  •84±n -27 

Angle  between  Collimator  and  Humpback  121  43  49 '53 

Azimuth  of  Humpback  303  25  24  -37 

43.  MOORp;,    NORTH    CAROLINA. 

,^3=36°  23'-9.  A=8o°   i7'-o. 

The  SimmstraiLsit,  Coa.st  Survey  No.  8,  was  mounted  in  the  meridian  of  the  triangu- 
lation station,  7  feet  to  the  north.  Focal  length  of  telescope  i"''io,  clear  aperture 
7'™,  magnifying  power  45,  pivot  inequality  for  clamp  west  +o"'-o2;  resulting  value  of 
one  division  of  eyepiece  micrometer  before  November  15,  o"'487o  and  after  chang- 
ing focus  to  the  close  of  the  series  o" -4804^0" '0002.  Value  of  one  divi.sion  of 
level  B  =  i"ii. 

In  connection  with  the  observations  for  time,  those  for  azimuth  jiroper  consist  of 
raicrometric  measures  between  the  verticals  of  the  star  and  mark.  The  light  at  the 
mark  was  shown  through  a  %-inch  aperture;  it  was  distant  from  the  station  5>^ 
miles  and  appeared  under  an  angle  of  depre.s.sion  of  2°  25'. 

A  set  of  observations  generally  consisted  of  7  or  11  transits  { times  noted  by  a 
.sidereal  chronometer)  of  the  star  over  the  micrometer  thread  set  in  advance  to  a  whole 
or  to  half  a  turn,  in.strument  clamp  west.  In  connection  with  the.se,  from  5  to  10  point- 
ings were  made  on  the  mark,  with  clamp  east,  and  the  same  number  with  clamp  west. 
The  level  was  recorded  with  each  .set.  When  measuring  the  horizontal  angle  between 
the  mark  and  the  line  to  Buffalo  the  transit  instrument  was  used  as  a  collimator.  The 
right  ascensions  of  the  stars  were  taken  from  the  best  .sources  available.  Ob.server, 
A.  T.  Mo.sman.  Probable  error  of  a  single  result  for  azimuth  as  derived  from  all  the 
stars  ±i"'io. 


THE    ASTRONOMIC    MEASURES. 


353 


Date. 

1K76. 


Sniiniiary  0/  tTsu//s  for  arjiiiml/i  al  iS/anyc,  Ni»ili  Carolina. 

ITlic  tabiilrir  rrsuUs  iiichKl 


Star  observed  near  up-      ,.     ,      .     .  ^ 
per  culmination.  ' '■^'^''  '•"'  '^• 


tile  correction  lor  cliiiriial  aberration.] 

Star  observed  near  low- 


Nov. 

i.S 

Nov. 

21 

Nov. 

22 

Nov. 

24 

Nov. 

26 

Dec. 
Dec. 

1 
2 

Dec. 

3 

Dec. 

,S 

1879  T.  Y.  C. 
a  Urs,  Min. 

I  r  Cephei 
79  Draconis 
a  Urs.  Min. 

/3  Cephei 

I I  Cephei 

a  Urs.  Min. 

Ti  Cephei 
226  Cephei 
a  Urs.  Min. 

II  Cephei 
79  Draconis 
226  Cephei 

79  Draconis 

II  Cephei 
79  Draconis 

V  Cephei 

a  Urs.  Min. 

II  Cephei 
79  Draconis 
y  Draconis 
4  163  Groom. 
a.  Urs.  Min. 

226  Cephei 

V  Cephei 

4  163  Groom, 
a  Urs.  Min. 


23  -96 
21-83 


22 '90 


21 -311 

24  •2kJ.22'99 

23  tA 

25  -o^l 

24  ■S9!-24'8o 
24-42] 

24  -241 
24-l6|23-07 
20 -Si  J 

22  81123 -53 
22 -63) 

26-68 

27-821 

26  63 

f25-20 

22  37 

23  •97] 


25 '15 


25  "99 

25'17 

24-17 

2573 

24-67 

26  -331 

22-691 
24-24] 


f24  -24 


Date. 

1876. 

er  ciilniii 

Nov. 

>.S 

I  Draconis 
32  Camelo. 

Nov. 

21 

I  Draconis 
32  Camelo. 

Nov. 

22 

I  Draconis 
g  Draconis 
32  Camelo. 

Nov. 

24 

1  Draconis 
9  Draconis 

Nov. 

26 

I  Draconis 
9  Draconis 
A  Draconis 

Dec. 

I 

9  Draconis 

Dec. 

2 

9  Draconis 
A  Draconis 
4  Draconis 
K  Draconis 
32  Camelo. 

Dec. 

3 

32  Urs.  Maj 
9  Draconis 
4  Draconis 
K  Draconis 
32  Camelo. 

Dec. 

5 

9  Draconis 
K  Draconis 
32  Camelo. 

.Mark  K.of  N. 


2.5  -691 
19  "63J 
24-84 
26'io 


22-66 


25 '47 


21 -21I 

21  ■9i>2o-89 

19-56J 


23  30 
22  -46 


22 -8S 


23  -22j 
22-63|23-2I 

23  -A 

23    15 


21  -37 
22-76 
22-71 
20-99 

■9  yi, 
22-54 

22  -.'^5 
20  92 

20  92 
>9"39 

23  -201 

21  •43>22-19 

21-94) 


21-44 


21  -26 


Dail}'  mean  values  of  mark  R.  of  N.  from  .stars  at  upper  and  at  lower  culminations: 


Nov.  15 

22  -78=^0  -55 

21 

24-23 

0-50 

22 

22-85 

045 

24 

22  -9S 

0-50 

26 

23  37 

0-45 

Dec.     I 

24-91 

0  -78 

2 

23  '32 

0-37 

3 

23  -20 

0-34 

5 

23  21 

0-42 

Weighted  mean 

23  -301^0  -15 

Azimuth  of  Mark 

Angle  between  Mark  and  Buffak-) 

Azinuith  of  Buffaki 


4192 — No.  7 — 02 23 


iSo    00     23 -30=1=0 -15 
21      26     52  -1 1 
•5S    33     3'    19 


354 


THE   EASTERN   OBLIQUE   ARC. 


44.    VOUNG,  NORTH    CAROLINA. 

<p=35°  44'  •4-  '^=80°  38'  -9. 

The  50'"'  direction  theodolite  ( Wiirdemann)  No.  3  was  mounted  over  the  triangula- 
tion  station.  The  azimuth  mark  was  placed  on  top  of  a  barn  on  Solomon  Hall  Place, 
distant  4'86  miles,  and  the  light  was  shown  through  an  aperture  Yi  inch  in  diameter.  A 
set  of  observations  con.sisted  of  a  pointing  on  the  mark,  telescope  direct,  2  observations, 
with  time  record  of  the  star,  one  pointing  with  image  direct,  the  other  with  image 
reflected  in  mercurj'.*  The  telescope  was  then  reversed  and  2  observations  on  star, 
direct  and  reflected,  and  a  pointing  of  the  mark,  telescope  reversed,  completed  the  set. 
Observer,  C.  O.  Boutelle.       Probable  error  of  a  single  result  for  azimuth  ±i"'i4. 

Suunnary  of  results  for  aziuiitth  at  Voitug,  North  Carolina. 


a  Ursa;  Minoris  at  various  hour  angles. 


a  Urs£e  Minoris  at  various  hour  angles. 


Date. 

Position 

Mark 
E.  of  N. 

Mean  by 
positions. 

Date 

Position. 

Mark 
E.  of  N. 

Mean  by 
positions. 

1S76. 

0    /        /' 

" 

1876 

0    /        // 

" 

Oct.     10 

'   I 

7  20  25-041 

Oct. 

12 

VI 

7  20  26 -091 

I 

26-20^ 

24 '33 

VI 

22-93[ 

23-76 

I 

21  75) 

VI 

22-26) 

II 

25-85] 

VII 

26 -071 
24 -72^ 

II 

23  79[ 

24-60 

VII 

24-87 

II 

24' 16) 

VII 

23-831 

Oct.    1 1 

III 

22  73 

VIII 

26-36I 

III 

22  '46 

23 '14 

VIII 

24 -78 1 

25  -68 

III 

24 '23 

VIII 

25 'Sgl 

IV 

25-08 

Oct. 

13 

IX 

26-211 

IV 

22-22 

23-29 

IX 

26-94^ 

25-68 

IV 

22 '57 

IX 

23 -88] 

V 

22-671 

X 

23-13] 
2I-94I 

V 

22-24! 

22-38 

X 

22-76 

V 

22-23] 

X 

XI 
XI 

XI 
Mean 

23-22I 

24-57 

26  -92 

27  -00 

26-16 
24-24  +  0' 

7  20 

•26 

0 

/           // 

Mean, 

Mark  east  of  north 

7 

20      24 

•24 

' 

Diurnal  aberration 

■+0 

31 

// 

Azimuth  of  Mark 

1S7 

20    24 

■55±o-26 

Angle 

between  Mark  and  Poore 

299 

32   29 

■14 

Azimuth  of  Poore 

126 

52    53 

•69 

*The  mercury  was  covered  by  a  mosquito  net  to  prevent  any  disturbance  of  the  surface  by  wind. 


THE    ASTRONOMIC    MEASURES. 


355 


45.    KING,  NORTH    CAROLINA. 


^  =  35       I2"2 


l=Hr~'    iH'-H. 


The  50'"'  direction  theodolite  No.  3  was  mounted  over  the  trianj^ulation  station. 
The  a/.imuth  mark  was  placed  on  the  roof  of  a  store  near  Kinj^s  Mountain  R.  R.  station, 
distant  2 "79  miles  from  King,  and  light  was  shown  from  a  bulls-eye  lantern  through  a 
hole  of  ^-inch  diameter.  A  set  of  olxservations  consisted  of  a  pointing  on  the  mark, 
telescope  direct,  2  observations  of  the  star,  one  with  image  direct,  the  other  with 
image  reflected  in  mercur}',  with  time  record.  The  instrument  was  then  reversed  and  2 
observations  of  the  star  were  made,  one  direct,  the  other  a  reflected  image,  and  one 
pointing  on  the  mark  concluded  the  set.  Observer,  C.  O.  Boutelle.  Probable  error  of  a 
single  result  for  azimuth  ±o"'98. 


Suiniiiary  of  results  for  azimuth  'it  Kina;,  North  Carolina. 


a  Ursse  Minoris  at  various  hour  angles. 


Date. 

Position. 

Mark 

W.  of  N. 

1877. 

0    /       " 

May       2S 

I 

40  01  07  '13 

I 

05-11 

I 

06-47 

II 

08-72 

II 

09-16 

II 

o6-i2 

May       39 

III 

05-90 

III 

06-24 

III 

P677 

IV 

06-71 

IV 

05 '99 

IV 

04-74 

V 

06-51 

V 

06 -21 

V 

06-49 

May       30 

VI 

06-90 

VI 

08-37 

VI 

09-31 

Mean   by 
positions. 


06  ■  2,1 


OS-QO 


06-30 


05-81 


06-40 


08-19 


a  Ursu;  Minoris  at  various  hour  angles. 


Date. 


1S77 


May 


May 


June 


Position. 

VII 

VII 

VII 
VIII 
VIII 
VIII 

IX 

IX 

IX 

X 

X 

X 

XI 

XI 

XI 

Mean 


Mark 
W.  of  N 


40  01  09-32 
05 '94 
06-70 
0S-14 
07-64 
05-60 
09 '3" 
09  "55 
09  02 
05 '25 
04-69 

05  50 
07-94 
07-91 

07-94 

40  01 


Mean  by 
positions. 


07  32 


07 'ij 


09-29 


05 'IS 


07  93 


07-07±o"-25 


Mean,  Mark  west  of  north 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Benn  * 

Azimuth  of  Benn 


40 

01 

07-07 
-  0-31      '/ 

139 

5S 

53 -24^0 -25 

I 

34 

43  7 

141 

33 

36  9 

*  This  angle  is  somewhat  uncertain  owing  to  large  corrections  to  directions  Young  and  Paris,  required  by  the 
adjustment  of  the  triangulatiou. 


i56 


THE    EASTERN    OBLIQUE    ARC. 


46.    PARIS,    SOUTH    CAROLINA. 


0=34°  56'-5- 


A  =82°   24' 7. 


The  50""  theodolite  No.  3  was  mounted  over  the  triangulation  station.  The  azimuth 
mark  was  i'4  miles  distant  from  the  station,  and  the  light  was  shown  through  an  open- 
ing one-half  inch  in  diameter.  A  set  of  observations  consisted  of  a  pointing  on  the 
mark  with  telescope  direct,  2  ob.servations  of  the  .star,  one  with  image  direct,  the  other 
with  image  reflected  in  mercury,  with  time  record.  The  instrument  was  then  reversed, 
and  2  more  ob,servations  of  the  star,  direct  and  reflected,  were  made,  and  the  set  was 
completed  by  an  observation  on  the  mark.  Observer,  C.  O.  Boutelle.  Probable  error 
of  a  single  result  for  azimuth  ±i"'i5. 

Smnniary  0/  results  for  azimuth  at  Paris,  South  Carotina. 


a  Ursx 

Minoris  at 

various  hour  angles. 

a  UrssE  Minoris  at 

various  hour 

angles. 

Date. 

Po.sition. 

Mark 
E.  of  N. 

Mea?i  hy 
positions. 

Date. 

Position. 

Mark 
E.  of  N. 

Mean  by 
positions. 

I'^75- 

0 

„ 

„ 

1875- 

0      '        // 

„ 

Oct.    23 

I 

'57 

59  59' 18 

Oct.    31 

VII 

157  59  64 ■ 76 

Oct      24 

I 
I 

58-54 
59 '25 

59-30 

VII 
VII 

62-16 
60  -84 

62  -59 

I 

60  -22 

Nov.      I 

VIII 

61  -15 

Oct.     25 

II 

58-05   ■ 

VIII 

61-95 

y         61.20 

II 

61-99 

►          60  -64 

VIII 

60-51 

II 

61  -88  , 

Nov.   17 

IX 

58  -37 

Oct.      2fi 

III 

59-75  ' 

I.X 

62-37 

\         61.05 

III 

64-61 

62-42 

IX 

62-41 

III 

62-90  . 

Nov.   iS 

X 

58-15 

Oct.    27 

IV 

59  -20  ' 

Nov.  20 

X 

61-16 

59-  54 

IV 

61-63 

60  40 

X 

59-31 

IV 

60-36 

XI 

61-88 

Oct.      2S 

V 

59-73  ■ 

60-98 
60-87 

XI 

62-63 

61.94 

V 
VI 
VI 

62-24  . 

59-63 

61-93 

XI 

Mean 

61  -31 

Oct.    30 

157  59 

60  -ggio"  -21 

VI 

61  -06  . 

Mean,  Mark  east  of  north 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  WofTord 

Azimuth  of  Wofford 


i5« 

00    GO  '99 

+0-31       " 

158 

00      01  '30^=0  '21 

70 

41      46-13 

267 

18      15-17 

THE    ASTRONOMIC    MEASURES. 


357 


47.    CMKkAHKlC,    GKOKCIA. 


(P=34°  3i''6. 


A  =83°  22' -6. 


The  50""  theodolite  No!  3  was  mounted  over  the  triaiij^ulation  station.  The  mark 
was  placed  on  the  roof  of  a  store  at  Toccoa  village,  distant  between  3  and  4  miles,  and 
was  about  600  feet  below  the  top  of  the  mountain;  the  liglit  was  sliown  throuj^h  an  open- 
injr  three-fourths  of  an  inch  in  diameter  and  appeared  under  an  anj^le  of  depression  of  less 
than  2° .  A  set  of  observations  consisted  of  a  pointing  on  tlie  mark  with  telescope  direct, 
2  observations  of  the  star,  one  by  direct  vision,  the  other  by  image  reflected  in  mer- 
cury, with  time  record.  The  instrument  was  then  reversed  and  the  preceding  ob.serva- 
tions  were  repeated  in  the  rever.se  order.  Observer,  C.  ().  Boutelle.  Probable  error  of  a 
single  result  for  azinuith  d=i"'47. 

SiiniiiKiiy  of  results,  for  azimidli  at  Ciiira/uT,  Ccorgia. 


Ursit  Miiioris  at  various  Iiour  angles. 


a  Ursie  Minoris  at  various  hour  aiiKles 


Date 

rositiou. 

Mr 
K.  0 

irk 

fN. 

Mean  by 
positions. 

Date. 

Position. 

Mark 
K.  of  X 

Mean  by 
positions. 

1874. 

0      ' 

,, 

1S7.I. 

0 

/ 

Oct.  2S 

I 

36    2C 

40 '63  1 

,, 

Nov.     2 

VII 

36 

20  38  36 

„ 

I 

39-60    . 

40  \\(^ 

VII 

38-3' 

38-67 

I 

41  -14 

VII 

39  34 

11 

38  -.ss  1 

Nov.     -t 

VIII 

36  -50  1 

II 

38 -.W   [ 

37  -77 

Nov.     6 

VIII 

36-58  [ 

36-i'> 

II 

36  42  J 

VIII 

35-39  ) 

Oct.   29 

III 

39  93 

Nov.    13 

IX 

32  50  1 

III 

38-32 

39-72 

I.\ 

33-15  [ 

32-89 

HI 

40-90 

I.\ 

33  02  J 

IV 

36  -74 

X 

40-28  1 

IV 

35-76 

36-12 

X 

37-01   \ 

37  -87 

IV 

35-85  . 

X 

36-3-  I 

Oct.  30 

v 

37-42 

Nov.   14 

XI 

35-77  1 

V 

37 -'4    ■ 

37-96 

Nov.   15 

XI 

35-51   [ 

36  06 

VI 
VI 

39-3' 
38-37] 
38 -45  I 

37 -Si 

XI 
Mean 

.;-s.,  1 

36 

20 

37  41  ±0" -4 

VI 

36-62  ) 

Mean,  Mark  east  of  north 

Diurnal  aberration 

Azimuth  of  INI  ark 

Angle  between  Mark  and  Rabun 

Azimuth  of  Rabun 


36 

20     37-41 

-fo-3i      " 

2X6 

20    37  -72^=0  -42 

331 

49     50-17 

iSS 

10     27  -89 

358 


THE    EASTERN    OBLIQUE    ARC 


48.    SAWNP;E,  GEORGIA. 


:  34°  14'   -I. 


A  =  84°  09'  7. 


The  75""  direction  theodolite  No.  i  was  mounted  over  the  triangulation  station. 
The  azimuth  mark  was  placed  on  a  hill  north  of  the  village  of  Ciimming,  2*7  miles  dis- 
tant from  Sawnee;  light  was  shown  through  a  half-inch  opening  and  appeared  under  an 
angle  of  depression  of  2°  38' '7.  A  set  of  observations  consisted  of  a  pointing  on  the 
mark  with  telescope  direct,  2  observations  of  the  star,  one  of  image  direct,  the  other 
of  image  reflected  in  mercurj-  with  time  record.  The  instrument  was  then  reversed  and 
the  preceding  observations  were  repeated  but  in  the  reverse  order.  Observer,  C.  O. 
Boutelle.     Probable  error  of  a  single  result  for  azimuth  zti""50. 

Siiiiniiajy  of  results  for  azimuih  at  Sanmee,  Georgia. 


a  UrscC  Minoris  at  varions  hour  angles. 


a  Ur.'«e  Minoris  at  various  hour  angles. 


Date. 

Position. 

Mark 
E.  of  N. 

Mean  by 
positions. 

Date. 

Position. 

Mark 
E.  of  N. 

Mean  by 
positions. 

1873- 

0      /        " 

,, 

1873- 

0      /        '/ 

" 

Oct.     13 

IV 

139  25  19  01 

Oct.    17 

I 

139  25  17 '96 

IV 

21-17 

I 

21-95 

IV 

19  67 

19-18 

I 

18-66 

20  -86 

IV 

17  90 

I 

21  -28 

IV 

18-15 

Oct.    21 

I 

24-47 

Oct.     14 

V 

17  '2.5 

II 

16-05 

V 

21  -62 

II 

18-75 

V 

22 -oS 

19.84 

II 

14-71 

16-67 

Oct.    15 

V 

16-07 

II 

16 -60 

^ 

V 

22-17 

II 

17-24  , 

VI 

'9  95 

Oct.    22 

III 

16  -90 

VI 

19-98 

III 

16-66 

VI 

18-31 

19  -05 

III 

16-01 

17-16 

VI 

17-62 

III 

19-12 

VI 
VII 

19-38 
20  -64 

III 
Mean 

17-13 

Oct.    16 

139  25 

19-06  +  0"  "41 

VII 

21  -18 

VII 

20-90 

20  -68 

VII 

21  00 

VII 

19-69 

Mean,  Mark  east  of  north 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  bet-ween  Mark  and  Currahee 

Azimuth  of  Currahee 


139 

25 

19  '06 
+0-31      " 

3'9 

25 

i9-37±o-4i 

286 

09 

06-75 

245 

34 

26-12 

i 


THE    ASTRONOMIC    MEASURES. 


359 


49.  ATLANTA  MIDDM-.  HASK,  CHORCIA. 

'fi=?,3°  54'  -3  A=84°   16'  "6. 

The  75""  theodolite  No.  i  was  mounted  over  tlie  trian^ulation  station.  Tlie  a/.i- 
mutli  mark  was  located  at  the  north  end  of  the  base,  3  miles  distant  from  Middle  Ha.se; 
li^ht  was  shown  throitj^h  a  half  inch  aperture.*  A  set  of  observations  consisted  of  a 
pointing  on  tlie  mark  with  telescope  direct,  2  observations  of  the  star,  one  observation 
with  star  direct,  the  other  with  image  reflected  in  mercury,  with  time  record.  Tlie  instru- 
ment was  then  reversed  and  the  preceding  operations  were  rejjeated,  l)ut  in  the  reverse 
order.     Observer,  C.  O.  Boutelle.      Probable  error  of  a  single  result  for  azimuth  ±i"'6i. 

Suiniiiarv  of  results  for  aziuiiilli  at  .Itlaiita  .^fiddle  Base,  Georgia. 


I'rsiL'  Minoris  ;\t  various  hour  anglts, 


<•  IrsiL  Minoris  at  various  hour  angles. 


1873- 
Jan,    1 


Jan. 


Jan.    14 


Jan.   21 


Jan.  23 


ition. 

Mark 
K.  of  N. 

0    '        " 

I 

52  08  03-16 

I 

04  '02 

I 

06-30 

I 

05 '37 

I 

04 '93  J 

II 

06-33 

II 

03 '35 

II 

04-92 

II 

03-90 

II 

03-70 

III 

07-82 

III 

08-99 

III 

10-47 

III 

09-26 

III 

II '23  J 

IV 

10 -01 

IV 

08  -75 

IV 

09-82 

IV 

09-96 

IV 

07  '37  J 

09-13 


Mean  by 
position. 

Dat 

f. 

Position. 

Mark 
E.of  N. 

" 

>873- 
Jan.   24 

v 

52  oS  10-16 

V 

07-12 

04-76 

V 
V 
V 

08-06 

05-4, 
05 '44 

Jan. 

27 

VI 

VI 

07  51 
08-35 

04-44 

Jan. 

3' 

VI 
VI 
VI 

oS  -82 
09-46 
II  08 

Keb. 

4 

VII 

07 -68 

Feb. 

5 

VII 

05  -oS 

09  55 

Feb. 

S 

VII 
VII 
VII 

04-97 

06 -S6 
04  '^3 

Mean 


Mean  by 
position. 


07-24 


09-04 


05" 


o7-i6±o"  -55 


Mean,  Mark  ea.st  of  north 

Diurnal  aberration 

Azimuth  of  Mark 

Reduction  to  ba.se  line 

Reduction  to  center  at  Northea.sl  Base 

Angle  between  Northeast  Rase  and  Stone  ^Mountain 

A/.inuith  of  Stone  Mountain 


52 

oS 

07  -16 
-0-31 

32 

oS 

07 '47 
-1  -Si 
-037 

So 

14 

23  65 

12 

22 

2S-94 

=0"  -55 


*The  .station  i.s  i  665  inches,  or  o"i-0423  to  the  west  and  north  out  of  line  of  the  base;  the  center  of  aperture  wasSmm-? 

east  of  Northeast  Base. 


. 


36o 


THE    EASTERN    OBLIQUE    ARC 


50.    I^AVENDER,  GEORGIA. 

<p=34°   19' -3  A=85°   17' -3 

The  30™  repeating  theodolite  No.  32  was  mounted  over  the  triangulation  .station. 
Focal  length  of  telescope  54"";  aperture  5"";  magnifying  power  28  and  48.*  The  azinmth 
mark  was  located  at  the  secondary  station  Coosa,  6'g  miles  distant,  and  nearly  at  the 
same  height  as  Lavender.  For  the  first  fifteen  nights  the  light  was  shown  through  a 
three-fourths  inch  opening;  after  that  it  was  enlarged  to  ly^  inches.  A  set  of  observa- 
tions con.sisted  of  12  repetitions  of  the  horizontal  angle  between  mark  and  star,  one-half 
of  these  with  telescope  direct  and  one-half  with  tele.scope  reversed,  and  observing  the 
star  alternately  direct  and  reflected  in  mercury.  Observer,  F.  P.  Webber.  Probable 
error  of  a  .single  result  for  azimuth  ±1"  '92. 

Simiuiarv  0/ irsiills  for  a~iiii!il/i  at  Lavender,  Ceori^ia. 


Date. 


a  UrsEE  Miiiori.s  at  various  hour  aii.sjles. 
Mark  E.  of  N. 


(1  Ursit  Minoris  at  various  hour  angles. 
Mark  E.  of  N. 


1874. 
Nov.        13 


Nov. 


Nov.       23 


Nov.       25 


153     16 


53  "25 
47-01 

52  "25 
51  '45 
48-40 
50-68 
44"27 
4S  -48 
46-37 
45  '26 
48-94 
44-46 
47  44 
47-06 
4371 


" 

187 

4- 

6-28 

Nov. 

25 

0  -04 

Nov. 

29 

5-28 

4 -48 

1-43 

371 

Nov. 

30 

2  -70 

I  "SI 

0  -60 

I  -71 

I  -97 

2  51 

Dec. 

2 

0-47 

0  -09 

3-26 

153  16 


41  -82 
43 '90 
49-62 

43 '03 
48  -  r  r 
47-27 

47-23 
46-94 
48-28 

44  -oo 
42-78 

45  73 
47-33 
47-08 


5-15 
3-07 
2-65 
3-94 
I  -14 
0-30 

0  -26 
0-03 

1  -31 
2-97 
4-19 
I  -24 
0-36 

O  -11 


Mean     153     16     46  -97^=0'''.  36 


Mean,  Mark  east  of  north  153  16  46  -97 

Diurnal  aberration  +0-31 

Azimuth  of  Mark  153  16  47  '28=^0".  36 

Angle  between  Mark  and  Kenesa-w  33  04  48-17 

Azimuth  of  Kenesaw                        -  300  11  59 'ii 


*Two  eyepiece.s  were  used  at  this  station. 


THE   ASTRONOMIC   MEASURES. 


361 


51.    AURORA,  AI.AIIAMA. 


<p=34°  08' -8. 


A =86°   ri'-o. 


The  30""  direction  theodolite  No.  108  (Troughton  &  Simms)  was  mounted  over  the 
triangulation  station.  Focal  length  of  telescope  o""75,  aperture  7'^""5,  magnif>  ing  power 
60.  This  instrument  was  used  here  for  the  first  time.*  The  azimuth  mark  was 
seen  under  an  angle  of  depression  of  0°  37' "3.  A  set  of  observations  consi.sted  of  a 
pointing  on  tlie  mark  with  telescope  direct,  followed  by  2  observ'ations  of  the  .star, 
one  with  image  direct,  the  other  with  image  reflected  in  mercury.  The  telescope  was 
then  reversed  and  the  star  and  mark  were  ob.served  as  before,  but  in  the  reverse  order. 
Observer,  F.  P.  Webber.     Probable  error  of  a  single  result  for  azimuth  ±3" '08  . 


Siiiiiiiiary  of  rcsiil/s /or  aziimil/i  0/ /lurora,  /llahaiiia. 


a  Ursce  Minoris  nt  v.'irious  liour  :uiKles. 


a  Urs;e  Minoris  at  various  hour  angles. 


Date. 

Position. 

Mark 
E.  of  N. 

Means. 

Datt 

Position, 

.       Mark 
E.  of  .N. 

Means. 

1877. 
June  19 

June  20 

I 

I 

0    / 
66  46 

50 '5 

49 '4 

1S77 
June 

25 

X 

X 

c     '         " 

66  46  467 

4S-3 

47-5 

II 
II 

45 '9 

42-8 

44 '3 

XI 
XI 

49  3 
507 

50  0 

III 
III 

43-8  1 
52  "4  1 

48-1 

XII 
XII 

53 '4 
52  3 

52  s 

IV 

54 '5 

53  7 

XIII 

5^-2 

57 '3 

June  24 

IV 

52 '9 

XIII 

564 

v 

V 

58-6 
59  9 

59  3 

June 

26 

XIV 
XIV 

54  9 
567 

55 -S 

VI 
VI 

54"4 
54 '9 

54-6 

XV 
XV 

5' -6 

527 

52  2 

VII 
VII 

47  7 
48-8 

48-2 

-XVI 
.XVI 

4Si 

4S7 

4'i-4 

VIII 

46-4 

.XVII 

47-0 

VIII 

42 '9 

44  7 

June 

27 

XVII 

5>2 

49  I 

IX 
IX 

47 '5 
44 '4 

46 '0 

Mean 

66 

46 

50-67±o"  72 

Mean,  Mark  east  of  north 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Brandon 

Azimuth  of  Brandon 


66     46     50  '67 
-0-31 
246     46     50-98     2=0" -72 

349     19    5«"37 
236    06     29  35 


*The  graduation  of  the  horizontal  circle  was  afterwards  found  to  be  defective 


l 


;62 


THE   EASTERN   OBLIQUE   ARC. 


52.    KAHATCHEE,    ALABAMA. 


<P=33     13    7- 


A  =86°  2 1 '-6. 


The  25""  repeating  theodolite  (Gambey)  No.  63  was  mounted  over  the  triangula- 
tion  station.  The  azimuth  mark  was  located  near  the  station  Horn,  distant  i7'3  miles; 
light  was  shown  from  a  signal  lamp.  A  set  of  observations  con.sisted  of  6  repetitions  of 
the  horizontal  angle  between  mark  and  star,  3  with  telescope  direct  and  3  with  telescope 
reversed,  with  the  requisite  time  and  level  readings.  One-third  of  the  sets  measured  the 
angle  .star  and  mark.  Value  of  one  division  of  level  =  2""67  at  24°  C.  Observer,  O.  B. 
French.      Probable  error  of  a  .single  result  for  azimuth  zho"'98. 

Suviinary  of  results  for  azimuth  at  Kahatchee,  Alabama. 


IX  UrScE  Minoris  at  various  hour  angles. 


June 


Date. 

1898. 


June 


Mark  E 

of  N. 

A 

Date. 

0          / 

// 

ti 

1S98. 

73  32 

12-3 

—  0  '2 

June 

7 

12  ■! 

~o-4 

June 

8 

137 

+  1-2 

11-8 

—0  7 

10 -s 

-I  7 

II  2 

-I  "3 

157 

+3-2 

12-3 

—0  '2 

15-6 

+3-: 

14  'O 

+  1-5 

14  "O 

+  1-5 

15  "I 

+  2-6 

13-4 

+0-9 

II  'O 

-I  '5 

June 

9 

13-6 

+  I-I 

09-4 

-3-1 

II -8 

-07 

II  -2 

-I  '3 

10-3 

—  2  -2 

Ursse  Minoris  at  various  hour  angles. 
Mark  E.  of  N, 


73     3 

2    09-8 

-27 

117 

-0-8 

12  -I 

-0-4 

127 

+0-2 

12-4 

— O'l 

13-0 

+0-5 

13-4 

+0-9 

13-0 

+0-5 

13 '9 

+  1-4 

13-6 

+  I-I 

12-1 

-0-4 

12-8 

+0-3 

12  -2 

-0-3 

117 

-0-8 

13-4 

+0-9 

II -6 

-0-9 

12 -I 

-0-4 

"•3 

—  I  '2 

Mean     73     32     12  •49±o''' •16 


Mean,  Mark  east  of  north 

Diurnal  aberration 

Azimuth  of  Mark 

Angle  between  Mark  and  Horn 

Azimuth  of  Horn 


73     32     1249 

+0-31       // 

253      32       I2"8ozbO'l6 

o  "00 

253      32       12  -So 


THK   ASTRONOMIC   MEASURES, 


363 


53.    ICTHKIOGK,  ALAItAMA. 


<f)  =  32°  a4''7. 


A  =  87°  <;3'-5. 


The  25'"'  repeating?  theodolite  (Gainbey)  No.  63  was  mounted  over  the  trian^ulation 
station.  The  aziniath  mark  was  placed  over  the  station  Lovers  Leap,  distant  1 52  miles. 
A  set  of  observations  consisted  of  6  repetitions  of  the  horizontal  angle  between  mark 
and  star,  3  with  telescope  direct  and  3  with  telescope  reversed,  with  tlie  requisite  time 
and  level  record.  One-half  of  the  sets  were  made  with  the  angle  mark  and  star,  the  other 
with  star  and  mark.  Value  of  one  division  of  level  2"'67  at  24"^  C.  Observer,  O.  B. 
French.     Probable  error  of  a  single  result  for  azimuth  ±o"'95. 

SuDimary  of  results  for  azimuth  of  lit/tridge,  Alabama. 

a  UrsEe  Minoris  at  various  hour  angles. 


Date. 

1S98. 
June       j6 


June       23 


Mark  E.  of  N. 


65      52 


46-9 
48-0 
46  'o 
50-0 
48-1 

45  7 
48-4 

49 '9 
48-9 

49  ■! 

48-4 
47 '6 
48-6 

49  "4 
47 '2 
49-8 


// 

+  2-1 

+  I-0 

+  3'o 

—  I  o 
+0-9 

+3  "3 
+0-6 
-0-9 
+0-I 

-  O  •! 

+0-6 
+  1-4 
+0-4 
-0-4 
+  1-8 
-0-8 


Date. 


a  rr.s;i;  Minoris  at  various  hour  angles. 
Mark  E.  of  N. 


June       23 
June       24 


65     52 


487 

+03 

47 '9 

+  I-I 

48-4 

-f-o-6 

50-0 

—  I  0 

50-0 

—  I  0 

49 '3 

—03 

5'   I 

—  2  I 

50-0 

—  I  0 

49 'o 

0  0 

50  0 

—  I  0 

5>   9 

-29 

49 '2 

— 02 

48-9 

+0-I 

49  "9 

-09 

50-0 

—  I  0 

51-6 

-2-6 

Mean     65     52     49  00±o"'i; 


Mean,  Mark  east  of  north  65     52     49 'oo 
Diurnal  aberration  -rO'3i        // 

Azimuth  of  Mark  245     52     49-3ii;=o-i7 
Angle  between  Mark  and  Lovers  Leap  o'txj 

Azimuth  of  Lovers  Leap  245     52     49 '3i 


364 


THE    EASTERN    OBLIQUE    ARC. 


54.     FORT    MORGAN,   ALABAMA. 


<P=30°   13'  'S- 


A  =88°  01' -4. 


The  60""  direction  theodolite  No.  2  (Troughton)  was  mounted  over  the  triangula- 
tion  station;  focal  length  of  telescope,  78^'";  aperture,  52"";  magnifying  power,  30  and 
40.*  A  set  of  okservations  consisted  generally  of  3  pointings  on  the  mark,  telescope 
direct,  and  3  pointings  on  same,  telescope  reversed;  from  3  to  6  observations  of  the  star, 
telescope  direct,  with  time  and  level  record.  The  instrument  was  then  reversed  and  the 
preceding  observations  of  star  and  mark  were  repeated,  l)ut  in  the  reverse  order.  Some 
sets  begin  and  end  with  6  pointings  on  the  mark,  the  reversal  of  the  instrument  taking 
place  in  the  middle  of  the  star  observations.  Value  of  one  division  of  level,  prior  to 
April  21,  i"'66;  after  that  date  2"'92.  Observer,  R.  H.  Fauntleroy.  Probable  error  of 
a  single  result  for  azimuth  =bo""75. 

Siiiinnary  of  results  for  aziinutli  at  Fort  Morgan,    Alabama. 


a  Ursce  Minoris  near  western  elongation. 


:  Ursoe  Minoris  near  eastern  elongation. 


Date. 

Position. 

Mark 
W.  of  N. 

J 

Dat 

e. 

Position. 

Mark 
W.  of  N. 

/J 

1847. 
Apr.    12 

I 

0       '         " 
151     44    59 '42 

+0-94 

1847. 
Apr.    12 

I 

151 

44 

59  32 

+0-72       . 

13 

II 

59 '16 

+1  -20 

16 

II 

58-48 

+  1-56 

May      5 

III 

62  '32 

-I  -96 

26 

III 

60-55 

-0-51 

9 

v 

59-64 

+0-72 

May 

9 

v 

60-67 

—0-63 

10 

IV 

61  '01 

—0  "65 

10 

IV 

61 -iS 

-I -14 

12 

II 

Mean 

60-58 

—0-22 
•33 

Mea 

n 

151     44     60-36  +  0" 

151 

44 

60  "04  ±0" 

■33 

0 

/ 

// 

Mean  of 

groups 

151 

44 

60 

•20 

Diurnal  aberration 

— 0 

•31 

// 

Azimuth  of  Mark 

28 

15 

GO 

•ii±o-23 

Angle  between  Mark  and  Cedar  Point 

115 

44 

45 

•50 

Azimutli  of  Cedar  Point 

143 

59 

45 

•61 

*  Two  eyepieces  used. 


THE   ASTRONOMIC   MEASURES 


365 


KAST    PASCAGOTII.A,   MISSISSIPPI. 


(p  =  30     2(r '7. 


A  =  88°  ,^2'-8. 


The  60'"'  direction  theodolite  No.  2  (Troughton)  was  mounted  over  the  triangula- 
tion  .station;  focal  length  of  telescope,  78'"';  aperture,  5 'a"'";  magnifying  ]>o\ver,  30 
and  40.*  A  set  of  observations  generally  consisted  of  6  pointings  on  the  mark, 
telescope  direct,  6  observations  of  the  star,  with  time  and  level  record.  The  instrument 
was  then  reversed  and  the  preceding  observations  were  repeated,  hut  in  the  reverse 
order.  One  divi.sion  of  level  ~2"'92.  Observer,  R.  H.  Fauntleroy.  Probable  error  of 
a  .single  result  for  azimuth  ±i"'i8. 

Suuimaiy  of  results  for  aziviiith  at  East  Pascaffoula,  Mississippi. 


a.  Ursa;  Minoris  near  eastern  elonKalion, 


Date. 

1847. 
June  12 
13 
14 
15 
iS 
24 


Position. 

II 

III 

I 

V 
IV 
V 


Mark 

W.  of  N. 


147  06  16 '97 
17 '55 
20  '10 
20  78 
18-17 
18-85 

147     06     iS-74±o"'4i 


a  Ursoc  Minoris  near  western  elongation. 


Mark 
W.  of  N. 


A 

Date. 

1S47. 

Po 

sition 

+  i'77 

June   14 

I 

+  1  -ly 

15 

III 

-1-36 

iS 

V 

—  2  -04 

26 

IV 

+0-57 

July     9 

II 

—  Q-II 

12 

III 

147    06     14-47 

19-04 
20-15 

IS -27 
17-90 
16-50 


+3-25 
-1-32 

-2-43 
-o'55 
-o-i8 
-f  I  -22 


147    06     i7-72±o"-55 


Mean  of  groups 
Diurnal  aberration 
Azimuth  of  Mark 


147     06     iS  -23 


32     53     42  -oSdrO  -34 


Angle  between  East  Pascagoula  and  Bayou  Casotte      96     22     50  Si 


Azimuth  of  Bayou  Casotte 


296     30     51  -27 


I 


*  Two  eyepieces  used. 


1 


366 


THE    EASTERN    OBLIQUE    ARC. 


56.    CAT    ISLAND    1S55,  MISSISSIPPI. 

<p  =  30°   14' -2.  A  =89°  04' -I. 

The  75""  transit  Coast  Survej'  No.  9  (Wurdeniann)  was  mounted  over  the  tri- 
angulation  station.  A  mark  was  placed  in  the  vertical  of  the  western  elongation,  and 
the  horizontal  difference  between  star  and  mark  measured  by  means  of  the  pivot  microm- 
eter, which  IS  ordinaril)-  employed  for  adjusting  the  transit  in  azimuth.*  A  set  of 
observations  consisted  of  2  pointings  on  the  mark  and  6  on  the  star,  with  time  and  level 
record,  one-half  of  these  observations  being  made  with  clamp  east,  the  other  with  clamp 
west.  Value  of  one  division  of  micrometer  2" "18,  and  of  one  division  of  level  2""o. 
Observ^er,  J.  E.  Hilgard.     Probable  error  of  a  single  result  for  azimuth  d=o""57. 

Su}iiinary  of  results  for  aziiiiuih  at  Cat  Island  /S^§,'\  Mississippi. 

a.  Ursse  ]VIi^ori^  near  western  elongation. 


Date. 

1855. 

Dec.  5 


Mark  W,  of  N. 


41 


Mean  i     41 


10  '20 

0971 
09  "55 
oS-8i 
oS  '33 
10 '58 
09  -53^0' 


— o  '67 
— o  tS 

—  O  '02 

+072 

-f  I  '20 
-I  -05 
•23 


Mean,  Mark  west  of  north  i  41 
Diurnal  aberration 

Azimuth  of  Mark  17S  18 

Angle  between  Mark  and  Missi.ssippi  City  13  52 

Azimuth  of  Mississippi  City  192  11 


// 

09  "53 
-0-31       // 

50  -ySdzo  -23 
23 '54 
14  "32 


*The  in.strument  was  overturned  in  a  storm  and  the  threads  of  its  diaphragm  were  broken;  a  new  single  thread 
was  put  in  and  served  for  the  time  and  azimuth  observations. 

fThe  triangulation  of  which  this  station  is  a  part  is  of  secondary  character  with  respect  to  size  and  precision, 
and  there  is  no  check  of  the  above  result  for  azimuth,  sue  as,  for  instance,  repeating  the  measures  on  other  dates.  The 
elongation  occurred  about  the  3d  of  the  above  6  consecutive  measures. 


PART     IV. 

DETERMINATION  OF  AN  OSCULATING  SPHEROID 

FOR  THE  REGION  COVERED  BY  THE 

TRIANGULATION. 

367 


>- 

UJ 

> 

cc 


2     CO     2 

ui 

•^    O    Q 
2    _    z 

or    '^   z 
<    °   5 

0-    o    ^ 

U     UJ     ^ 

£r   <  ^ 

H-    O    6 

o 

C/5 


DETERMINATION  OF  AN  OSCllLATIXi;  Si'HIiROII) 

FOR  THF:  KECION  COViiRED  BY  THE 

TRIAXGUEATIOX. 

A.   COMPARISONS  OF  THE  AvSTRONOiMIC  AND  GEODETIC  RESULTS  AT 
STATIONS  CONNECTED  WITH  THIi  OBLIQUE  ARC. 

Parts  II  and  III  contain  tlie  necessary  stateniuiUs  and  results  for  the  next  (jperation, 
namely,  the  direct  comparison  of  the  astronomic  latitudes,  longitudes,  and  azimutlis 
with  their  corresponding  values  derived  geodetically  by  development  of  the  triangulation 
upon  the  Clarke  spheroid  of  iS66.  In  doing  this  the  geodetic  data  for  the  station 
Hays,  Kansas,  as  given  in  the  account  of  the  transcontinental  triangidation  and  arc  of 
the  parallel  in  latitude  39°,  have  been  adhered  to.      The\'  are: 


[  (Po=  3'*^  54  S"'!'"^" 
\  A,,  =:  99  16  16  730 
I    "'=359  44   19 'cx)    Hays  lo  I^a  Crosse. 

We  shall  thus  .secure  .sy.stematic  positions  which,  if  desirable,  may  be  made  at  once 
available  for  a  determitiation  of  an  osculating  spheroid  ba.sed  upon  a  surface  of  witler 
geographic  limits  than  is  contemplated  in  this  di.scussion. 

As  early  as  the  year  1879  the  writer  made  a  preliminary  compari.son  of  tlie  astro- 
nomic and  geodetic  measures  then  available.*  The  stations  inchuled  extend  from 
Calais,  Maine,  to  Atlanta,  Georgia.  That  di.scu.ssion  furni.shed  the  first  comprehensive 
information  of  the  relative  magnitude  and  distribution  of  the  outstanding  differences 
between  the  astronomic  and  geodetic  results  in  the  United  States,  the  latter  as  develojKnl 
on  each  of  two  reference  spheroids.  It  led  to  the  adojnion  of  the  Clarke  .spheroid  of 
1866  for  u.se  by  the  Coast  and  (xeodetic  Survey. 

As  a  matter  of  general  interest,  the  location  oi  the  ])rincipal  ,irc  measures  and  areas 
oi  osculating  spheroids  is  .shown  on  a  Lambert  equivalent  zenithal  projection  ujxmi  a 
meridional  plane  and  transferred  from  a  hemi-  to  a  plani-.sjihere,''- constructed  by  Adolph 
Lindenkohl,  of  the  Drawing  Division,  Coast  and  Geodetic  Survey,  for  this  special  u.se. 
Lambert  himself  pointed  out  how  the  whole  surface  of  the  sphere  could  lx.»  represented, 
a  fact  .stated  again  in  Littrow's  admirable  work,  Chorographie,  etc.,  von  J.  J.  Littrow. 
Wien,  1833,  page  126. 


*U.  ,S.  Co.isl  ;m(l  OtoiUtic  .Siirvty  K<iniit  for  1S70.  .VniKiuiix  No.  8,  pp.  IIO-123. 

4192 — No.  7 — 02 24 


3<^ 


370  THE    EASTERN    OBLIQUE    ARC. 

I.  The  Astronomic  Latitude  Stations. 

The  foUowinc^  table  of  the  comparison  of  the  astronomic  and  geodetic  determina- 
tions of  latitudes  consists  of  the  collection  of  the  latitude  results  derived  from  direct 
observation,  given  in  full  in  Part  II L  To  these  results  have  been  added  the  reduction 
to  sea  level,  and  the  reduction  to  the  average  position  of  the  earth's  pole  of  rotation. 
The  tabular  geodetic  latitude  is  that  of  the  corresponding  astronomic  station,  the  local 
reduction  for  any  difference  of  position  between  the  two  stations  having  been  applied. 

The  reduction  to  sea  level. — As  a  consequence  of  the  earth's  rotation  producing  a 
slight  curvature  of  the  vertical  of  a  station  in  the  plane  of  the  meridian  concave  toward 
the  pole,  a  small  correction  to  the  observed  latitude  is  required,  which  is  given  b}-  the 
expression 

/=  —  gsVu  /'  sin  2  qj 

where  h,  or  height,  is  given  in  meters  and  /  in  seconds  of  arc.      The  value  of  the  factor 
—  0^000  172  sin  2  cp  for  different  latitudes  is  as  stated  below: 

For  (p  - 


50° 

—  o"'ooo  169 

45 

172 

40 

167 

35 

161 

30 

149 

The  reduction  for  variation  of  pole. — The  advisabilitj- of  introducing  into  the  present 
discussion  of  the  astronomic  and  geodetic  measures  corrections  for  variation  in  the  posi- 
tion of  the  earth's  axis  of  rotation  largely  depended  upon  the  degree  of  reliability  of 
the  values  of  such  corrections.  The  origin  of  this  motion  is  at  this  time  imperfectly 
understood,  and  the  uncertainty  in  the  correction  for  variation  is  here  considerably  . 
increased  on  account  of  the  early  dates  of  many  of  our  latitude  observations,  some  dating 
back  more  than  half  a  century. 

In  consequence  of  the  importance  of  the  subject  the  International  Geodetic  Associa- 
tion for  the  measurement  of  the  earth  has  organized  a  special  service  for  the  purpose  of 
procuring  data  for  the  study  and  elucidation  of  the  law  of  this  variation  which  was  first 
definitely  formulated  by  Dr.  S.  C.  Chandler.  The  association  .selected  a  small  number  of 
.stations  suitably  located  around  the  earth,  near  the  parallel  of  north  latitude,  39°  08'  10", 
at  which  it  is  intended  to  prosecute  refined  latitude  observations  for  a  series  of  years. 
The  range  of  the  variation  is  small,  about  o"'3  from  a  mean  value,  and  it  requires,  con- 
sequently, the  utmost  attainable  precision  as  regards  instruments  and  method  in  order  to 
bring  its  periods  and  ranges  into  clear  evidence.* 

The  probable  error  of  a  correction  to  an  observ^ed  latitude  may  be  estimated  at 
d=o"'04  for  the  past  decade,  but  for  the  earlier  dates  of  our  observations  this  needs  to 
be  increased. 

The.se  small  corrections  for  variation  of  latitude,  while  yet  very  uncertain,  could  have 
no  sensible  infiuence  upon  the  results  of  this  investigation  for  determining  a  represent- 
ative .spheroid,  nor  would  these  small  corrections  be  of  any  consequence  in  connection 


*When  comparing  Dr.  Chandler's  predicted  resu'ts  of  the  motion  of  the  pole  for  the  years  1890  to  18975.^,  with 
result.s  deduced  directly  from  observation,  a  comparatively  large  discord  is  noticed  in  some  places,  as  might  be  expected 
in  such  an  inquiry,  nor  are  these  modern  observations  free  from  considerable  uncertainty. 


I 


' 


THK    DETERMINATION    OF    THF.    SI'HKkOIl>.  371 

witli  the  local  deflections  of  the  vertical,  the  average  inagnitiule  of  wliich,  nanielj',  2"'4,* 
has  been  deduced  from  a  large  number  of  comjjarisons.  It  lias,  however,  been  concluded 
to  apply  these  small  and  as  3'et  rather  uncertain  corrections  in  the  present  investigation. 
The  corrections  to  all  latitude  results  were  computed  by  Chandler's  formulae t  except 
for  a  few  .stations  where  none  were  needed  and  for  four  stations  (Kxupied  in  1IS97  and 
1898  where  Dr.  Albrccht's  results  were  introduced  in  jireference,  as  contained  in  his 
report  on  the  state  (jf  the  latitude  \ariation  at  the  close  of  the  year  1899  [Centralbureau 
der  Internationalen  ludmessung,  Berlin.    1900]. 

About  one-half  of  the  corrections  thus  computed  were  found  to  be  belcnv  o"' i ,  a 
very  few  reached  o""2,  and  none  exceeded  o"'25.  I"or  the  whole  arc  these  corrections 
balance. 

The  effect  of  the  \ariation  of  the  po.sition  of  the  pole  upon  observed  differences  of 
longitude  is  small  enough  to  be  negligible  and  the  .same  is  true  with  reference  to  the 
observed  azimuths,  for  which  the  j^robable  error  of  observation  always  exceeds  the  small 
correction  due  to  the  polar  variation. 

The  headings  of  the  following  summar}-  of  results  need  no  e.xiilanation.  The  geo- 
detic latitudes  were  in  all  cases  referred  to  the  astronomic  station  unless  the  two  stations 
happened  to  be  located  on  the  .same  parallel  or  to  be  identical  in  position.  The  relative 
position  of  the  stations  is  stated  in  the  preceding  abstracts  and  the  reductions  there 
given  are  applied  to  the  geodetic  latitude  with  the  sign  reversed.  The  last  colunni  con- 
tains the  apparent  local  deflection  of  the  vertical  in  the  plane  of  the  meridian  or  the  dif- 
ference (A-G)  of  the  two  values  in  the  two  preceding  cohunns. 


*  Probable  error  in  the  direction  of  the  vertical   from   all   parts  of   India   except   portions   under   Hinialay  in 

attraction  is  about  +  2"'8.     (Annual  Report  of  the  Survey  of  India,  1803-94.) 

t  Astronomical  Journal  (Gould's),  No.  446.  October  14.  1S9S.     The  formula:  are.  for  the  coordinates. 

ix=ii  sin  (/-Ti)  fl  + 0-095  sin  (©-308°) 
\y  =  1 1  cos  (/  — Ti)  9  +0110  cos  (0—     3°) 

Where 

Ti  =  2  412  646  +  427  o  E  —  o  -oS  E  = 

e     =  0° -.Sij  +  o -ooo  316  E 

1 1  =  o"  '125  +  o'o5  sin  (2  414  363  —  /)  x  o°-oi5 

Here  t  and  Ti  are  expressed  in  Julian  dales,  /  is  the  epoch  of  observation,  Ti  any  epoch  when  the  pole  of  the  figure 
passes  the  Greenwich  meridian  between  Greenwich  and  the  instantaneous  pole  of  rotation  1  this /<»//<•/  taken  as  the 
origin  of  the  coordinates  .r  and.v),  K  is  the  number  of  periods,  t»  Uic  daily  auirular  motiiui,  / ,  the  radius  vector,  and  J"  the 
sun's  longitude  at  the  time  /. 

The  variation  of  latitude  /ip  =  ip  ~  <po  =  .«'  .sin  A  -  _)■  cos  A.  where  A  equals  the  longitude  of  the  place  uist  of  Green- 
wich. <p  the  obsened  and  ipo  the  corrected  latitude,  as  referred  to  the  average  or  fixed  position  of  the  pole. 

The  day  number  in  the  expression  for  Ti  corresponds  to  the  ist  of  July,  iSg;.  and  that  in  parenthesis  in  the  expres- 
sion for  /I  to  the  14th  of  March.  iSgS.     The  direction  of  the  motion  of  the  pole  is  from  west  to  east. 


372 


THE    EASTERN    OBLIQUE    ARC. 


Conipm-isoii  of  astronomic  and  ocodiiic  latitudes. 


No.    Name  of  latitude  station.  State. 


Calais 

Cooper 

Humpback 

Bangor 

Farinington 

Mount  Harris 

Howard 

Mount  Desert 

Ragged  Mountain 

Sabattus 

Mount  Pleasant 

Cape  Small 

Mount  Independence 

Gunstock 

Againenticus 

Isles  of  Shoals 

Unkonoonuc 

Thompson 

Wachusett 

Cambridge,     Harvard 
College  Observatory 

Cambridge,     Cloverden 
Observatory 

Mount  Tom 

Manoinet 

Sand  ford 

West  Hills 

New  York 

Beacon  Hill 

Mount  Rose 

Yard 

Principio 

Maryland  Heights 

Pooles  Island 

Sugar  Loaf 

Dover 

Webb 

Rockville 

Soper 

Taylor 

Strasburg 

Cape  May 

Causten,  Washington 

U.  S.  new  Naval  Observ- 
atory, Washington. 

Hill 

U.  S.  old  Naval    Observ- 
atory, Washington 

Seaton,  Washington 
U.  S.  Coast  and  Geodetic 
Survey     Office,    Wash- 
ington 

Bull  Run 


Me. 

Me. 
Me. 
Me. 
Me. 

Me, 

Me. 

Me. 

Me. 

Me. 

Me. 

Me. 

Me. 
N.  H. 

Me. 

Me. 
N.  H. 
Mass. 
Mass. 
Mass. 


Year  and  month  of 
observation. 


1557  Sept. 

1559  Sept. 

1558  July  and  Aug. 
1857  Sept.  and  Oct. 
1S66  Oct.  and  Nov. 

1855  Aug.  and  Sept. 
1859  July 

1856  Aug.,  Sept.,  Oct. 
1854  Aug.,  Sept.,  Oct. 
1S53  June  and  July 
1851  July  and  Aug. 
1851  Sept.  and  Oct. 
1849  Sept.  and  Oct. 

1560  July  and  Aug. 
1S47  Sept.,  Oct.,  Nov. 

1547  Aug. 

1548  Sept.  and  Oct. 
1846  Sept.  and  Oct. 
i860  Sept.,  Oct. 
1844,  1845 


Reiluction — 

Seconds— 

Observed 

astronomic 

latitude. 

To  sea 
level. 

To 

average 

pole. 

Of  as- 
tronomic 
latitude. 

Of  geo- 
detic lat- 
itude * 

A-G 

0     ' 
45  II 

09-40 

— o-oi 

0  -00 

09-39 

03 -78 

4-5-6' 

44  ,S9 

12  60 

—0-04 

—0-07 

12-49 

11-53 

4-0-96 

44  51 

47  -.56 

— Q-oS 

—on 

47  '37 

49-20 

- 1  -83 

44  4'^ 

12-87 

— o-oi 

-1-0 -03 

12-89 

14-19 

—  I  -30 

44  40 

19  '54 

—0-12 

— o'o7 

19 '35 

20-78 

-I  -43 

44  39 

54  -66 

—0-07 

4-0-09 

54-68 

52-71 

4-1-97 

44  .37 

49- -24 

—  o-oi 

—0  -06 

49'I7 

45-24 

4-3  -93 

44  21 

06  -51 

-o-oS 

-1-0-09 

06-52 

05-19 

+  1-33 

44  12 

42-96 

—0  '07 

+0-04 

42-93 

43-03 

— o-io 

44  08 

37  73 

—0  -04 

—0-02 

37  '67 

36-01 

4-1 -66 

44  01 

36-44 

—  o-ii 

—0  -09 

36-24 

34  -65 

+ 1  -.59 

43  46 

43  '69 

-    O-OI 

-ho  -02 

43  70 

41  -45 

+  2-25 

43  4.5 

34  '47 

—  0  -03 

4-0-12 

34 '56 

31-80 

4-2-76 

43  31 

03-81 

—012 

4-0-02 

03-71 

00-98 

+  2-73 

43  13 

24-96 

-0-04 

0  -00 

24-92 

22-75 

4-2-17 

42  .59 

12-97 

0  -00 

0  -00 

12-97 

12-87 

4-0-10 

42  58 

59  '54 

—0-07 

-1-0-07 

59 '34 

57-85 

+  1-49 

42  36 

38-02 

—001 

~o  -03 

37-98 

39-68 

-1-70 

42  29 

16-13 

—  0  -10 

—  O'OI 

16-02 

17-80 

-1-78 

42  22 

48-05 

—  0  "01 

48  -04 

51-48 

-3-44 

Mass.     1S55  Aug..  Sept.,  Oct.      42  22  40-97 


Mass.  1S62  July  and  Aug. 

Mass.  1867  July  and  A.ng. 

Conn.  1S62  Sept.  and  Oct. 

N.  Y.  1865  Aug. 

N.  Y.  185S  June 

J^-  J-  1875  July  and  Aug. 

N.  J.  1852  July 

Pa.  1S54  Oct.,  Nov. 

Md.  1S66  July,  Aug.,  Sept. 

Md.  1S70  Sept.,  Oct.,  Nov. 

Md.  1S47  June  and  July 

Md.  1879  Oct. 

Del.  1897  May 

Md.  1850  Oct.  and  Nov. 

Md.  1-891,  1S92 

Md.  1850  June  and  July 

Md.  1847  May 

Va.  1881  June 

N.J.  1S81  May,  1891  May 

D.C.  1851  May  and  June 

D.  C.  1893  May,   1S97  June, 
1S93,  1894,  1895,  1896 

Md.  1850  Aug.  and  Sept. 

D.C.  1861  to  1864,  1866  to 
1 888,  1893 

D.C.  1850  June 

D.C.  1S91  .-^ug.,  1S92  Aug., 
1S94  Aug. 

Va.  1871  Sept.  and  Oct. 


42_I4  27-62 
41  55  35-35 
41  27  40-47 
40  48  50  -06 
40  43  48 -39 
40  22  27 -81 
40  22  05-41 
39  58  29-39 
39  35  32-81 
39  20  32-10 
39  17  17-52 
39  15  49 '71 
39  09  13-62 
39  05  25-21 
39  05  10-45 
39  05  10-69 
38  59  46-08 
38  59  31  -49 
38  55  44  -69 
38  55  32-18 
38  55  13-91 

38  53  52-31 
38  53  38 -79 

38  53  25-20 
38  53  07  -43 


-o  -06 
-o  -02 
-0-05 
-002 
0-00 
-o  -02 

-0-02 
-0-03 

-o  -01 

-o  -07 

0  "00 

-0-07 

o  -00 

-0-01 

-0-03 

-O  "02 
-O  "OI 
-0-03 

o  -00 

-0-02 
-O-OI 

-O-OI 
-0-01 

Q-OO 
0-00 


4-0-06 
4-0-08 
4-0-15 

—  0-12 
-0-13 
4-0-14 

—  0-09 
4-0-03 
-0-05 

4-0-16 
0  -00 

—  o-io 

-0-15 

H-0-I5 

—  0-06 
o  -oo 

4-0-10 
~o  -06 

—  0-14 

—  o  -16 

4-0  -06 


-0  -oS 
-o  -08 


.38  52  56-79         -0-07 


40  -96 

27-62 
35-41 
40-57 
49-92 
48-26 
27-93 
05-30 
29-39 
32-75 
32-19 
17-52 
49-54 
13-47 
25-35 
10  -42 
10  -61 
46-07 
31-56 
44-63 
32-02 
13-74 

52  -36 
38-78 

25-12 
07-35 


56-72 


44-28 

27-84 
,36  -71 
41-13 
53  -28 
49-16 
24-46 
01  -30 
22-67 
34  -55 
26-30 
13-52 
43-65 
18 -,59 
24  -16 
09  -08 
09  -80 
46-34 
27  -82 
46-53 
32  -81 
14-89 

52-24 
40-12 

26-82 
10 '00 


52  -oS 


-3-32 

—  0-22 
-1-30 
--0-56 
-3-36 

—  0-90 
4-3-47 

4-4  -00 

4-6-72 

- 1  -80 

+5-89 
4-4-00 
+5-89 
-5-12 
4-1  -19 
+  1-34 
4-0-81 

—  0-27 
4-3-74 

—  I  -90 

-0-79 
-I -15 

+0-12 
-I '34 

-1-70 
-2-65 


4-4-64 


*  For  reference  data  see  introductory  remarks  to  Part  IV. 


THE   DETERMINATION   OF    THE   SPHEROID. 


373 


Coiiiparhon  of  astn)iio)nic  aud  geodetic  latitudrs  -  Coiilimitd. 


No.    Name  of  latitude  stritinii.   State. 


Year  ami  inonlli  of 
observation. 


(Jh.served 

astroiioinic 

latitude. 


Reduction- 


Seconds- 


To  sea  '""  <^ii  ^^       Of  geo- 

I(  V.-1        averaKe  troiiomic  detic  lat- 

^  pole        latitude,      itude. 


A-G 


Cape  Henlojjen 
Clark 

Elliott  Knob 
Charlottesville,      McCor- 

mick  Observatory 
Long  Mountain 
Moore 
Young 
King 
Paris 
Currahee 
Lavender 
Sawnee 
Aurora 

Atlanta  Middle  Base 
Atlanta 
Kahatchee 
Montgomery 
Lower  Peach  Tree 
Coon 
Mobile 

Ea.st  Pascagoula 
Fort  Morgan 
New  Orleans 


Md.  1846  June,    1849   May 

and  June 

Del.  1897  Sept. 

\'a.  1871  July,  Aug. 

Va.  iSyS  July 

Va.  18S2  Aug. 

Va.  1S75  Oct.  and  Nov. 

N.  C.  1876  Nov.  and  Dec. 

N.  C.  1876  Oct. 

N.C.  1876  Dec. 

S.C.  1875  Oct. 

Ga.  1874  Sept.  and  Oct. 

Ga.  1874  Oct.  and  Nov. 

Ga.  1S73  Oct.  and  Nov. 

Ala.  1877  May  and  June 

Ga.  1S72  Sept. 

Ga.  i8SoJan. 

Ala.  i8g8  June 

Ala.  1856  Mar.  and  A])r. 

Ala.  1857  Apr. 

Ala.  1898  May 

Ala.  1856  Dec. 

Miss.  1847  June  and  July 

Ala.  1S47  Mar.  and  Apr. 

La.  1858  Jan.  and  Peb. 


38  52  25 '12         — o'oi 


38  46  40  'oo 
38  18  39-80 
3«  09  57 '5' 
38  01  60 '95 

37  17  2S72 
36  23  54 'ys 

35  44  2''.i" 
35  "2  ■3'3i 

34  .56  3>'9'' 

.34  31  37  75 

.34  19  '5'«' 

34  14  04 ■20 

34  oS  47  -45 

33  54  21 -82 

33  44  59 '3" 

33  13  39 'yo 

32  22  45-41 

31  50  21  -ly 

3!  14  47-82 

30  41  33  42 

30  20  40  -92 

30  13  47  -89 

2Q    S7    25  -  2S 


o  -00 

—  O  -ijA 
— O  -23 
— o  -03 

—0-07 

-o.  13 
— o  -05 
-O-OH 

—  Q-IO 

— o  -08 
— o'oS 

—  o  -10 
—0-07 
— o  -05 
—0-04 
— o  -06 

—  O  'Ol 

—  0-02 
— Q-O! 

o  -00 

O  -QO 

o  -00 
O  -oo 


—  0  -12 

— o  -14 

—  O  "20 
+  0-17 

+0-19 
+  0-23 
+0-24 
+  0-19 
+  0-19 
+0-07 
+  0-02 

—  007 
+0-25 

— o-ii 

+  0-02 

—  Q-IO 
— O'ifi 

— ot; 
— 007 

+  0-IO 

— 0-ot 
— o-oi 

+  1-)  -OS 


25  05 

39-8H 
.39-60 

57  ■»'' 
61  •(>-) 

28 -84 

55  '05 

21  -69 
13   42 

32  -OS 
37  74 
1575 
04-03 

47  '63 
21-66 

59  iS 
39  74 
45 '24 
21  -00 

47  74 

33  52 
40-91 

47  ■•'*8 
?>  -5^ 


25-68 

39  ^-^ 
39-22 
.57 '51 
.55-9' 

25  '.I'" 
5'  44 
12-27 
09  S"* 

27  -S8 
36-64 
16  01 
02  -93 

45  24 
19  -05 
56-10 
35  9' 
37  37 
iS-si 

48-39 
2.8-91 

33  59 

40  -30 


-0-63 

—  o'lo 
+0-JI 
-043 
H-S-ls 

•t-3  34 
■r3-6l 
+  9-42 
■+-3"'4 
+4  17 
+  1  -pj 
—0-26 
+  1  -lo 

+  2-39 

+  2-61 

~3''3 

-2-49 
-0-65 
+4 '61 
+  7-32 

■4-7  ■5'^ 
-I---,, 


Revicic  of  tlic  preceding  latitudinal  deflections. — Takin}>^  in  the  whole*  iuunlx;r  of 
comparisons,  there  is  a  preponderance  of  phis  si^ns  in  the  vahies  of  (A-G),  viz:  44  with 
a  +  and  27wath  a  —  sign.  This  inequality  is  most  marked  in  the  southern  part  of  tlie 
arc  where  the  po-sitive  signs  predominate,  and  this  is  e.si)ecially  the  ca.se  for  stations  near 
the  Gulf  coast.  The  mean  deflection  of  the  last  4  stations  is +6" '6,  apparently  indi- 
cating a  deviation  of  the  plumb  line  directed  toward  the  Gulf.      The  average  value  of 

112 
{A-G)  is  +— --  =  +  i""6.      There  are  .several  localities  where  the  latitude  stations  are 

crowded  together,  and,  consequently,  are  .subject  to  the  same  regional  deviation.  For 
each  of  these  localities  it  is  de.siral)le  to  substitute  a  single  station  of  average  or  repre- 
sentative value.  There  are  6  such  cases,  the  latitudes  in  each  group  being  contained 
within  a  space  of  about  i'.      For  these  groups  we  have  adopted  the  following  \-alues: 

Groups. 

20,  21 

27.  28 
35.  36,  37 

3'"^-  39 

40,  41,  42 

43,  44,  45,  46,  47,  4S 

These  values,  when  substituted  for  the  respective  tabular  numbers,  make 

::fi^A-G)     ,  106 

=  H ^=  -+- 1    "8  nearh'. 

"  59 


Value  0 

.-!-(;. 

// 

-3  -JS 

+3 

73 

+  1 

•11 

+  1 

•74 

—  I 

•2S 

—0 

•26 

374 


THE    EASTERN    OBLIQUE    ARC. 


Of  these  differences  39  are  positive  and  20  negative.  The  resulting  average  (  + 1""8) 
may  be  regarded  as  representing  the  difference  between  the  standard  latitude  of  the 
transcontinental  arc  of  the  parallel  of  39°  and  that  of  the  eastern  oblique  arc.  This 
discordance  of  nearly  2"  in  the  standard  latitudes  of  the  arcs  at  their  intersection  is 
not  surprising  when  we  examine  the  regional  changes  in  the  values  of  (A-G)  along  the 
arc  of  the  parallel.  There  are  109  astronomic  latitudes  connected  with  the  arc  of  the 
parallel  and  71  with  the  oblique  arc.  Of  these,  24  are  common  to  both;  consequently, 
156  independent  latitude  stations  are  involved  in  the  discussions  of  the  two  arcs. 

2.  The  Astronomic  Longitude  St.\tions. 
Coniparihon  of  astronomic  and  standard  geodetic  longitudes. 


No. 

Name  of  longitude  station 
and  state. 

Object  of  reference. 

Observed 
astronomic 
longitude. 

Seconds 
of  geo- 
detic lon- 
gitude.* 

A-G. 

I 

Calais,  Me. 

Transit 

0     ■ 
67 

16  ,S7'86 

53 '92 

+  3 '94 

2 

Bangor,  Me. 

Transit 

68 

47  02 -60 

01  -20 

-1-1  -40 

3 

Cambridge,  Mass. 

Center  of  dome,  Harvard  Observatory. 

71 

07  45-69 

44  74 

+0-95 

4 

Cape  May,  N.  J. 

Transit 

74  55  45 'SB 

48-03 

-2 '35 

5 

Dover,  Del. 

Transit 

75 

31   18-45 

24 '51 

-6-06 

6 

Washington,  D.  C. 

Seaton,  transit 

76 

59  52  '73 

60  10 

-7-37 

7 

Washington,  D.  C. 

Coast  and  Geodetic  Survey  Office,  transit 

77 

00  25  64 

3271 

-7-07 

S 

Washington,  D.  C. 

Old  Naval  Observatory,  small  dome 

77 

03  02-30 

06-68 

-4 '38 

9 

Washington,  D.  C. 

New  Naval  Observatory,  center  clock  room 

77 

03  56-76 

62-80 

—6-04 

0 

Strasburg,  Va. 

Transit 

7S 

21  3570 

39  '54 

-3-84 

1 

Charlottesville,  Va. 

McCormick  Obser\-atory,  transit 

78 

31    20-10 

21-15 

-1-05 

2 

Statesville,  N.  C. 

Transit,  near  Simenton  College 

80 

53  41 -31 

40-44 

-Ho -87 

3 

Atlanta,  Ga. 

Transit,  1S96 

84 

23  20  07 

19-41 

-ho -66 

4 

Montgomery,  Ala. 

Transit 

86 

17  59 '19 

60-92 

-173 

[5 

Lower  Peach  Tree, 

Ala. 

Transit 

87 

32  40 -94 

43  '37 

-2-43 

[6 

Mobile,  Ala. 

Transit 

88 

02  37-37 

33  -83 

+3  54 

17 

New  Orleans,  I,a, 

Transit,  iSSo  and  1S95,  Lafayette  Square 

go  04  II '44 

12  -16 

-0-72 

Review  of  the  preceding  longitudinal  deflections. — Before  examining  the  tabular  val- 
ues {A  —  G)  it  is  de-sirable  to  contract  the  table  on  account  of  the  regional  deflections 
about  Washington  by  admitting  only  one  in  the  place  of  the  four  closely  packed  stations. 
The  average  value  of  {A  —  G)  for  numbers  6,  7,  8,  9  is  — 6"-22.  For  the.se,  number  9 
or  the  New  Naval  Observatory  value  —6" '04  has  been  substituted.  The  distribution  of 
the  14  stations  over  the  whole  arc  is  fairly  uniform.  They  .show  an  average  deflection 
Qf  c^j[^Q)  —  _o"-92,  the  plumb  line  apparently  being  attracted  to  the  westward. 
This  amount  might  be  expected  from  the  location  of  the  arc.  Thus  for  one-half  of  the 
stations,  either  on  account  of  proximity  to  the  Atlantic  coast  or  in  con.sequence  of 
their  location  to  the  ea.st  of  the  principal  mountain  chains,  or  for  both  reasons,  negative 
values  of  {A—G)  might  be  expected.     The.se  values  are  as  follows: 


Cambridge 

Cape  May 

Dover 

Washington 

StrasVjtirg 

Charlottesville 

Statesville 


+0-95 
-2-35 
-6 -06 
—  6-04 
-3'S4 
- 1  '05 
+0-87 


Average  value  =  — 2''-50. 


♦For  reference  date  see  introductory  remarks  to  Part  IV. 


THE    DETERMINATION   OF   THE    SI'HI-.kOID. 


375 


Thu  value  at  New  Orleans  also  has  a  nej^ative  sign,  though  tlie  alxjve  reasons  do 
not  aj)ply  to  this  location. 

It  has  already  been  remarked  in  the  account  of  the  transcontinental  triangulation 
and  arc  of  the  parallel  in  latitude  39°  that  Cape  May,  though  directly  located  on  the 
coast,  is  distant  about  2 13  kilometers  (115  nautical  miles)  from  the  actual,  but  submerged, 
continental  border.*  At  Calais  we  find  the  largest,  yet  moderate,  jxjsitive  deflection 
+  3" "94,  which  probably,  in  a  mea.sure,  is  due  to  the  attraction  of  the  mass  of  Xova 
Scotia  lying  directly  to  the  ea.stward  of  the  station.  Respecting  the  remaining  6 
stations  no  .special  features  appear  to  be  present,  and  the  deviations  may  be  indiflferently 
+  or  — ,  the  average  value  being  +o"'45. 


3.  The  A.stkonomic  A/amith  St.vtions. 
Comparison  of  as/ronoiiiir  and  i^iodc/ic  arjiiiiii//is  of  sides  of  the  tiiani^ulalion. 


Year 

No. 

Name  of  aziimiUi  station. 

State. 

of 
observa- 
tion. 

Reference  .station. 

Astronomic 

azimuth 

of  line. 

Geodetic       ,    ,. 
azimuth.t  ''"^• 

I 

Cooper 

Me. 

1859 

Howard 

0 
35  > 

53 

1 2  05 

09-93 

-i-2-l2 

2 

Howard 

Me. 

1859 

Pigeon 

63 

54 

45" 

42-96 

4-2-15 

3 

Humpback 

Me. 

1858 

Cooper 

254 

42 

32-36 

27-80 

-1-4-56 

4 

Mount  De.sert 

Me. 

1856 

Ragged  Mountain 

78 

30 

46-57 

45-89 

-i-o-68 

5 

Mount  Harris 

Me. 

1S55 

Humpback 

254 

35 

10-62 

06  04 

+4-58 

6 

Ragged  Mountain 

Me. 

1854 

Mount  Pleasant 

Si 

48 

45-00 

41-73 

+3-27 

7 

Cape  Small 

Me. 

1851 

Sabattus 

'53 

18 

63  •51 

59-9 

+3-6 

8 

Sabattus 

Me. 

1853 

Mount  Independence 

24 

31 

23-5' 

20-64 

-1-2-87 

9 

Mount  Independence 

Me. 

1S49 

Agamenticus 

26 

55 

48-60 

48-58 

4-0 -22 

10 

Mount  Plea.sant 

Me. 

185 1 

Mount  Blue 

205 

59 

21-56 

'7-53 

4-4-03 

II 

Agamenticus 

Me. 

1.S47 

Thompson 

2 

5fi 

55  '51 

55-92 

-0-41 

12 

Gunstock 

N.  H. 

1S60 

Mount  Pleasant 

217 

43 

33-60 

27-36 

-1-6-24 

13 

Unkonoonuc 

N.  H. 

184S 

Onnstock 

196 

.35 

20-38 

16 -68 

+  3-70 

14 

Thompson 

Mass. 

1S46 

Manomet 

35> 

21 

41-86 

40-40 

-I-I-46 

1.5 

Wachusett 

Mass. 

i860 

Bald  Hill 

24 

17 

41-45 

32-42 

-9  03 

16 

Har\'ard  Observatory  (dome) 

Ma.ss. 

1869 

Blue  Hill 

356 

25 

264 

25  1 

+  '-J 

17 

Blue  Hill 

Mass. 

iS4,S 

Manomet 

305 

57 

30-05 

29  89 

■fo-i6 

18 

Shootflying 

Mass. 

1S45 

Manomet 

M3 

03 

22-74 

■9  5 

+3-2 

19 

Indian 

Mass. 

1845 

Copecut 

135 

35 

58-82 

62-6 

-3-8 

20 

Copecut 

Mass. 

1S44 

Blue  Hill 

"75 

17 

06-5 

04-04 

-1-2-5 

21 

Beaconpole 

R.I. 

1S44 

Blue  Hill 

22S 

55 

17-24 

'7-53 

-0-29 

22 

Spencer 

R.I. 

1S44 

Beaconpole 

185 

57 

33-02 

36-5 

-3-5 

23 

Mount  Tom 

Mass. 

1S62 

Monadnock 

212 

37 

21-74 

'5 -'3 

4-6-61 

24 

Sandford 

Conn. 

1S62 

Ruland 

5 

50 

25-28 

15 -86 

4-9-42 

25 

West  Hills 

N.   Y. 

1865 

Woostcr 

174 

57 

3S-32 

33  87 

4-4-45 

26 

Beacon  Hill 

N.J. 

1875 

Weasel 

183 

35 

29  89 

29  32 

4-0-57 

27 

Mount  Rose 

N.J. 

1852 

Mount  Holly 

7 

46 

55-59 

58-26 

-2  67 

28 

Yard 

Pa. 

•854 

Lippiucott 

547 

17 

38  -57 

37-09 

4-1 -48 

29 

Priucipio 

Md. 

1866 

Turkey 

1 

34 

43-5' 

34  59 

4-  8 -92 

30 

Cape  Henlopen  Light-House 

Del. 

1S97 

Brandy  wine  Light- 1  louse 

'73 

45 

■7-33 

15-29 

4-2-04 

3' 

Marriott 

Md. 

iSjg 

Hill 

96 

37 

43-36 

35-04 

4-   S-32 

32 

Webb 

Md. 

1  S,SO 

Soper 

SS 

59 

49 '24 

42-70 

4-   654 

33 

Hill 

Md. 

1S50 

Webb 

319 

46 

5789 

51  -13 

4-  6-76 

34 

Soper 

Md. 

1  ^.so 

Webb 

a6S 

49 

23  -46 

IS -14 

+  5-3» 

3.S 

Seaton 

DC. 

l.Soy 

Hill 

265 

32 

53-76 

42-33 

4- II -45 

36 

Causten 

n.  C. 

l,-;?! 

Soper 

2IO 

54 

41-78 

58-3 

4-   3-5 

37 

Sugar  Loaf 

Md. 

1879 

Bull  Run 

32 

29 

16-79 

22 -jS 

-   5-49 

3S 

Maryland  Heights 

Md. 

1870 

Bull  Run 

35S 

43 

06 -SS 

'O-54 

-  5-«6 

*  Page  S37  of  Special  Publication  No.  4.     "  The  Transcontinental  Triangulation.' 

t  For  reference  data  see  introductory  remarks  to  Part  IV. 


376 


THE    EASTERN    OBLIQUE    ARC. 


Comparison  of  asfronoinic  and  geodetic  aziiiiuths  of  sides  of  the  triangulation 


Name  of  azimuth  station. 


39 

Bull  Run 

40 

Clark 

41 

Long  Mountain 

42 

Elliott  Knob 

43 

Moore 

44 

Young- 

45 

King 

46 

Paris 

47 

Currahee 

43 

Sawnee 

49 

Atlanta  Middle  Base 

50 

Lavender 

51 

Aurora 

52 

Kahatchee 

53 

Ethridge 

54 

Fort  Morgan 

55 

East  Pascagoula 

56 

Cat  Island  1S55 

Year 

State. 

of 
observa- 

Reference 

tion. 

Va. 

i,S7i 

Peach  Grove 

Va. 

1871 

Bull  Run 

Va. 

1S75 

Spear 

Va. 

1S78 

Humpback 

N.C. 

1S76 

Buffalo 

N.C. 

1S76 

Poore 

N.C. 

i«77 

Benu 

S.  C, 

i'"*75 

Wofford 

Ga. 

1S74 

Rabun 

Ga. 

'873 

Currahee 

Ga. 

1873 

Stone  Mountain 

Ga. 

1S74 

Kenesaw 

Ala. 

1S77 

Brandon 

Ala. 

189S 

Horn 

Ala. 

189S 

Lovers  Leap 

Ala, 

1847 

Cedar  Point 

Miss. 

1847 

Bayou  Casotte 

Miss. 

1S55 

Mississippi  City 

IgU 

'att 

();/~continiieii 

Astronomic 
azimuth 
of  line. 

Geodetic 
a-/dmuth. 

A-G. 

0 
263 

53 

2S-15 

30-60 

-  2-45 

202 

19 

2777 

28-81 

-   1-04 

223 

2S 

4174 

46  -62 

-  4-88 

303 

25 

24  '37 

22-28 

+   2-09 

158 

33 

3''I9 

32-10 

—  0-91 

126 

52 

33  '69 

52-65 

+  I  -04 

141 

33 

36-9 

39 '3 

-  2-4 

267 

18 

I5'I7 

15-89 

—  0-72 

tSS 

10 

27-89 

26-00 

+  I -89 

245 

34 

26-12 

28-93 

-  2-81 

312 

22 

28-94 

32-71 

-  3  77 

300 

1 1 

59'il 

61 -oS 

-  1-97 

236 

06 

29 '35 

31  '43 

-    2-oS 

253 

32 

1 2  -80 

15 '48 

-  2-68 

245 

52 

49 '31 

52-05 

-  2-74 

143 

59 

45 '61 

50-69 

-  5-08 

296 

30 

51 '27 

53-20 

-   1-93 

192 

II 

14-3 

08  -4 

+5-9(?) 

Revieii'  of  the  preceding  aziviuthal  deflections. — We  recognize  as  their  main  feature 
systematic  but  small  po.sitive  deflections,  i.  e.,  plumb  line  attracted  westward  for  that 
part  of  the  arc  which  lies  north  of  the  thirty-ninth  parallel,  and  small  negative  deflec- 
tions for  the  part  .south  of  that  parallel,  thus  showing  for  the  whole  arc  a  small  predomi- 

86-7 


nating    plus   value 


or      


+  i"-55.      Omitting  the  last  azimuth,  No. 


n  56 

56,  as  doubtful,*  and  using  No.  33  in.stead  of  the  six  closely  clustered  values  in  the 
vicinity  of  Washington,   i.   e. ,   Nos.  31,  32,  t,},,   34,  35,  36,   the  average  value  for  the 

oljlique    arc    becomes        ^ = -|-  =+o"-9i.      This   represents   the  discrepancy 

between  the  average  azimuths  of  the  arc  of  the  parallel  in  latitude  39°  and  of  the  oblique 
arc,  and,  considering  its  small  size,  the  general  azimuthal  directions  of  the  two  arcs  may 
be  taken  as  being  in  satisfactor\-  accord.  A  remarkable  feature  in  the  tabular  values  of 
(A-G),  and  one  that  had  been  known  for  a  long  time,  is  the  large  regional  deflection 
existing  in  that  part  of  the  triangulation  common  to  the  two  arcs.  The  average  deflec- 
tion observed  at  the  six  .stations — Marriott,  Webb,  Hill,  Soper,  Seaton,  and  Causten — is 
+  7"'o,  the  plumb  line  being  attracted  to  the  westward.  If  we  convert  this  value  into 
a  corresponding  longitudinal  quantity,  we  have  JA=  — z/«/sin  <^=  — ii""i,  which 
agrees  in  sign  but  exceeds  in  amount  the  mean  value  {A-G)  =  —6"'2,  as  found  from 
the  four  longitudinal  deflections  in  this  region  obtained  at  stations,  only  one  of  which 
is  identical  with  any  of  those  named  above. 

Considering  that  the  present  adopted  azimuth  depends  upon  73  azimuth  determina- 
tions or  stations  of  the  triangulation  along  the  39th  parallel,  any  new  or  independent 
correction  that  might  Ije  deduced  for  standard  value  in  the  oblique  arc  would  probably 
not  differ  from  it  h\  as  much  as  one  .second. 


*The  last  value  of  our  table  is  marked  as  doubtful  for  the  reason  that  the  accuracy  both  of  the  astronomic  and 
geodetic  measures  is  inferior  to  that  of  the  other  tabular  re.sults;  and.  moreover,  its  appearance  with  a  large  positive 
value  (pointing  to  westerly  deflection)  in  a  region  where  minus  values  predominate  imparts  to  it  an  anomalous  char- 
.acter,  especially  in  a  flat  region  of  quaternary  formation  without  any  surface  indications  to  justify  or  account  for  a 
reversal  in  the  direction  of  the  disturbed  noiiual  of  the  place.  No  further  use  will  be  made  of  this  station  iii  coiinec- 
lion  with  azimuths 


' — v^ 


,/  » 


THE   DETERMINATION   OK   THE   SI'HHROIO.  377 

B.  DETERMINATION  OF  A  SPHICROII)  MOST  NEARLY  RIv PRI-SKXTIXO 
THAT  PART  OF  THE  EARTH'S  SURFACE  LYINO  BETWi:i:x  MAIXl- 
AND  LOUISIANA  AND  ALONG  THE  REGION  COYERED  HY  THE 
TRIANGULATION. 

The  )ii(tliod  and  fonuitltr  employed. 

After  having  assumed  a  reference  sj)heroicl  representing  the  figure  of  the  eartli  as 
closely  as  may  be,  and  placed  in  position  thereon,  and  having  developed  the  triangula- 
tion  upon  its  surface,  the  problem  next  to  be  solved  is  t(j  determine  corrections  to  the 
dimensions  of  the  reference  spheroid  whicli  shall  make  the  sum  (jf  the  squares  of  tlie 
apparent  discrepancies  between  geodetic  and  astronomic  results  a  minimum.  In  other 
words,  we  are  to  determine  a  representative  or  ()sculator\-  spheroid  wliich  shall  most 
nearly  harmonize  these  measures,  necessarily  lea\ing  outstanding  the  mere  local  deflec- 
tions of  the  vertical  at  the  stations  involved. 

For  this  purpo.se  it  has  been  thought  most  expedient  to  follow  the  theoretical 
development  as  presented  by  Capt.  A.  R.  Clarke,  R.  E.,  in  the  Aeeounl  of  the  Principal 
Triangulatiou  of  Great  Britain  and  Ireland/-  In  this  work  the  method  is  developed 
and  applied  to  the  computation  of  a  spheroid  who.se  (Hmensions  were  in  l)est  accord 
with  the  curvature  of  the  surface  of  tliese  countries. 

Let  P  beany  point  on  the  actual  irregular  or  disturbed  surface  (2)  and  /'_  its 
projection  upon  the  surface  of  a  regular  or  reference  spheroid  (  i  ) ;  through  /'  on  the 
surface  (2)  let  a  sy.stem  of  rectangular  axes  of  coordinates  <*;',  /;,  T,  lie  drawn,  so  that 
B,  is  directed  to  the  north,  //to  the  east,  and  C^  to  the  zenith.  For  an\-  two  points  A 
and  B  connected  b>-  triangulatiou  let  f/^  if'  l)e  their  observed  or  apparent  latitudes,  JA 
their  observed  or  apparent  difference  of  longitude;  also,  let  the  direction  of  the  meridian 
be  observed  at  each  place.  If  A,,  B,  are  the  projections  of  A  and  B  and  .s-  their  distance, 
and  OL  the  observed  azimuth  of  B  at  A,  and  a'  the  reverse  a/.inuuli,  or  that  of  A  at  B. 
and  if  ^,,  ^/,  «,,  ^v/,  and  A\^  refer  to  the  points  A,,  B,,  then 

<i',  =  (H  //  tan  t^i         ((/  =  <('  •  /;'  Ian  (p' 
-JA,  =  _/A     //'  sfc  ip'  1  //  sec  ip 

Also  let  {(p'),  («''),  (^A),  be  the  munerical  results  which  should  olitain  for  the  point  B 
by  starting  the  computation  from  the  observed  latitude  and  given  longitude  of  A  ami 
the  observed  direction  of  the  mericUan  at  A,  together  witli  the  known  distance  .<.  then 
the  following  relations  will  hold.  They  are  the  funilamental  e(|Uations  (,iS),  jxige  b2o 
of  the  Ordnance  vSurvex'  publication  mentioned  alK)\-e.  i 

z'  =  ((p'\     <p'  '  (COS  J,U?  '  (sin  </)  sin  JA)/;     {      cosii/  j  6'i  ■  Of 

\ 

-sec  cp';/'  =  (  JA)     JA  .  (Ian  <,V  sin  JA)4     (^^,^^^  ,,-,cos</>'     """"-^ '*" )  "  ■  (sec  (p'  sui  <«,')30 

,    .       , ,  /sin  <p  cos  JX\ 

tan  </)'//'  =  (  a')      <r'     (sec  e^^' sm  JA  );     (  .^^  a,'        )"     (tan  <<>' sm  <»' )d6 


*Orilii;uiCf  Survey,  l.oiuloti,  is^S.  pp.  6ck)  ;uu1  folUnviiii;.     .Sec  ;i1mi  Chapli-r  \U  of  Cl;>rke'<  G«rcKlesy;  (Oxford.  iSCSa 
tcr,  Hclmert,  Uoherc  OcoiUUic,  Vol.  i,  pp.  ,s,vS-5,;'v     I.fip/ig,  iSSo, 


378  THE    EASTERN    OBLIQUE    ARC. 

where 

These  equations  may  be  written  in  the  form: 

The  values  of  the  absolute  terms  are: 

,ti  =  ( calculated    -observed)  latitude 

;f,=  (observed  — calculated)  longitudexcos  q>' 

;^,=  (calculated— observed)  aziiuuthXcot  <p' 

Here  ^  =  deflection  of  the  vertical  in  the  plane  of  the  meridian  at  the  initial  station, 
positive  when  the  tangent  to  the  actual  surface  is  elevated  to  the  north  of 
the  station. 
//= deflection  of  the  vertical  in  the  plane  at  right  angles  to  the  meridian  at  the 
initial  station,  positive  when  the  tangent  to  the  actual  surface  is  elevated 
to  the  eastward. 

Similarly  B'  and  //'  represent  deflections  of  the  vertical  in  the  meridian  and  in  the  prime 
vertical  planes  for  any  other  point  whose  latitude  is  q)\  the  latitude  of  the 
initial  point  being  q). 

H  is  the  arc  distance  of  the  initial  point  from  any  other  point. 

a,  the  azimuth  at  the  initial  point  of  any  other  point. 

a',  the  reverse  azimuth  or  that  from  any  point  to  the  initial  one.  The  azimuths  count 
from  north  toward  the  east. 

JA  is  the  difference  of  longitude  between  the  initial  and  any  other  point;  west  longi- 
tudes are  considered  positive;   ^A.  =  A'  —  A. 
It  may  be  remarked  here  that  the  observations  for  difference  of  longitude  give  the 

.same  kind  of  information  as  those  for  azimuth,  so  that  the  first  set  of  equations  may 

be  u.sed  as  a  confirmation  or  check  of  the  other  set. 

The  quantities  ^,  «,  a' ,  (p,  qj' ,  JA  are  geodetic  values. 

For  evaluating  the  quantities  Qs  and  Sfl  in  the  preceding  equations,  we  have  for  v 

or  length  of  line  normal  to  the  surface  and  terminating  at  the  minor  axis 

_  a 

( i—e-  &\n-  (pY'^ 
and  for  p  the  radius  of  curvature 


/■>-- 


Putting 
hence 


(i—c^  sin^  ^)''^ 


looil  =  /,       and       ^-       '""^    cos^  'U{(p+5(p')=n' 
_        [i-g°  sin'^  V,((pM-<P)]'°      ,j,„j         /  _(joo)'  cos'  'U((p+3<P') 


(i_^^2)(i_^2si„3<p)>/2  M         {i-ey 

also  writing 

/^(arc  icjo")  for/  and  t'(arc  100'^)  for  f,  then 
Qe=/.i'{q>'—<p)  sin  i"li 
—  5&=icxDGsin  I'^w+ioo^'- 0  sin  i"v. 


THE   DETERMINATION   OF   THE   SPHEROID.  379 

where  ^  is  a  constant,  viz: 

_    Vs  sin  =<p 
^~ i—e^  sin»  qi 

If  «  =  equatorial  radius  of  reference  spheroid  and  (?"=  the  square  of  its  eccen- 

tricity,  the  respective  vahies  of  the  corrected  spheroid  become 

rt   I  ya  and  c"  ■   t 

The  corrections  to  the  semiaxis  major  and  to  the  square  of  the  eccentricity  are 

then 

a  (arc  ioo")«  and  (arc  u-ni"  )v 

where  ic  and  v  are  to  be  derived  from  the  sohition  (A  the  equations. 

The  coefficients  in  the  equations  (18)  in  simphfied  form  are  as  follows: 

rt,=cos  A\  f (72=  — sin  q>'  sin  A\ 

bi=?>\\\  <p  sin  AX  6,=cos  ip'/cos  (/3— (sin  0  cos  it')  tan  (p 

Ci=n  0  cos  a'  fj=ioo  fj  sin  a' 

(f'i.  =  ICX3  ;/■  0  sin  a' 


fi=/-ij^  Scos  (.r'+/<'(<^— tp) 


<?,=:— sin  JA  sin  <p' 
(^,=sin  </)  cos  J  A,  sin  g/ 
f,=  ioo  0  sin  it' 
e^=ioo g  fj  sin  a' 


The  values  of  ^  and  a'  are  to  be  computed  from  the  known  oreodetic  latitudes  and 
longitudes  of  the  initial  and  any  other  astronomic  point  of  the  triangulation.  ^  and  a' 
may  be  computed  by  the  inversion  of  the  formulae  for  direct  position  computation  as 
given  in  the  Report  for  1894,  Appendix  No.  9,  pages  284-2S6.  No  extreme  accuracy 
is  required  in  the  computation  of  the  respective  coefficients,  and  it  is  found  that  the 
Survey  formulae  when  rigorously  employed  in  their  reversed  ai)plicati<)n — viz,  given 
two  positions  to  find  their  distance  and  azinuiths — answer  well  up  to  the  limit  here 
required*  where  ^  does  not  exceed  14°. 

The  values  of  /^  and  yu'  are  to  be  tabulated  for  convenient  intervals  of  latitude  and 
of  sufficient  extent  to  cover  the  limits  of  the  triangulation. 

In  applying  the  preceding  method  and  formulae  for  the  determination  of  an  improved 
.spheroid  most  nearly  conforming  to  the  surface  under  con.sideration,  a  suitable  initial 
station  must  be  chosen,  preferably  centrally  located  in  order  to  keep  the  values  of  ^  as 
small  as  possible.  The  Lnited  States  (New)  Naval  Observatory  on  Georgetown  Heights. 
\Va,shington,  Di.strict  of  Columbia,  has  been  adopted  for  this  station:  its  geographic 
position  refers  to  the  center  of  the  clock  room,  for  which  we  have  the  geodetic  latitude 
38°  55'  I4"'89  and  the  geodeti'  longitude  77°  04'  o2"'8o,  the.se  figures  being  based 
upon  the  .same  data  as  the  positions  in  the  transcontinental  triangulation. t  In  this 
system  the  position  of  .station  Hays,  Kan.sas,  is  in  latitude  38°  54'  50"' 180  and  in  longi- 
tude 99°  16'  1 6" "730.  The  maximum  value  of  H  for  the  extreme  northea.st  station  is  less 
than  10°  and  for  the  extreme  .southwest  .station  slightly  le.ss  than  14'-''.  The  initial 
station  also  fairly  represents  an  average  local  deflection  of  the  plumb  line  for  the  region 
about  the  Di.strict  of  Colnml)ia,  and  the  point  being  connnon  to  the  two  arcs,  additional 
equations  of  condition,  depending  upon  other  stations  of  the  arc  of  the  parallel  than 
those  at  present  included,  can  reatlily  lie  incorporated,  if  desirable. 


♦The  additional  terms  in  ^qt  given  on  p.  iSs  ninst  be  incUidetl  in  the  c\<nipntation.  .\  ixmgh  check  on  #  anil  a  may 
he  had  by  the  nse  of  the  spheric.il  formnliv,  cos  tf-cos  «>  ct)S  •}>'  cos  J\  i-sin  ii>  sin  «>'  and  sin  a  -cvvs  ip  sin  J,\  sin  • 

tThe  new  ol)seivatory  was  connected  by  local  trianKiilation  with  the  Coast  and  Oeoiletic  Sur\-ey  trianindalion  by 
Prof.  W.  Harkne.ss,  .\.strononiical  Director  in  iSo,;  and  :Sai,  and  by  .Assistant  K.  l>.  Preston  in  is»i4.  The  work  of  .\.v»-»tant 
C.  Jnnken  in  iSSi  is  involved  in  the  adjustment  of  the  v;oodetic  connection. 


38o 


THE    EASTERN    OBLIQUE    ARC. 


Collection  of  certain  constants  and  tabular  quantities  required  in  the  computation  for  establishing  the 

conditional  equations. 

For  Clarke's  spheroid  of  1866  we  have 

log  a  =  6  '804  698  57 
log  b  =  6  '803  223  78 
log  ^==7 -830  502  57 

with  the  following  data  for  the  reference  station, 

<P  =  2fi°  55'   14" -9 
A  =  77    04    02    "8 

logir  =  9'296  391 
Values  of  log  n  sin  1"  hetiveen  latitudes  jo°  and  4^°. 


<P' 
2,0° 
30 'A 
31 

31V2 
32 

3254 

33 

33 '4 
34 
34  >^ 


6-687  692  I  35"= 


J(^)°  =  iS-3 


674 

353^ 

655 

36 

637 

36>^ 

619 

37 

600 

37  K 

582 

38 

564 

■38^ 

546 

39 

527 

39'-^ 

'^{'A 


6-687  509 
490 
471 
453 
434 
415 
396 
377 
359 
340 

°  =  i8-8 


(P 
40° 
4-O^A 
41 

4i>^ 
42 

42K 
43 

43  K 
44 

44  M 
45 


6-687  321 
302 
283 
264 

245 
226 
207 
188 
169 
150 
131 


TH]-;    I)]-,TKRMINATION    OF    THK    SI'HF.kOII). 


3«I 


Values  of  lo,i(  ii'  sin  i"  lichvi'fu  latitudes  ^i>^  atid  ./^l^ 


qj' 

3o°oo' 

6  '544  (K) 

lo 

42  Si 

20 

41  61 

30 

•540  41 

40 

39  2(1 

50 

37  99 

31 

•536  77 

10 

35  54 

20 

34  31 

30 

■533  07 

40 

3  J  S3 

50 

30  5'^^ 

32 

•529  33 

10 

2S  07 

20 

26  80 

30 

•525  52 

40 

24  24 

50 

22  95 

33 

•521  66 

10 

20  36 

20 

1 9  06 

30 

•517  75 

40 

■6  43 

50 

15  'I 

34 

•513  7^ 

10 

12  44 

20 

I  I  \o 

30 

•509  75 

40 

08  41) 

50 

07  04 

35 

6  -505  67 

du/ 

<p' 

35 

=(X/ 

6-5'J5  67 

119 

ro 

04  30 

120 

20 

02  92 

1 20 

3" 

■5"'  54 

121 

40 

■5'X)  15 

121 

5" 

•49«  75 

122 

36 

■497  34 

123 

10 

95  93 

123 

20 

94  51 

124 

30 

■493  "9 

124 

40 

91  66 

'25 

5" 

90  22 

'25 

37 

•488  78 

126 

127 
128 

]<) 

«7  33 

20 

•^5  «7 

1 28 

30 

■484  41 

40 

82  94 

1 29 

50 

81  46 

129 

3« 

■479  9'^ 

130 

10 

78  49 

130 

20 

76  99 

131 

30 

•475  49 

132 

40 

73  9^ 

132 

5" 

72  46 

133 

39 

•470  94 

134 

10 

69  41 

'34 

20 

67  88 

'35 

3" 

■466  34 

135 

40 

64  79 

136 

50 

63  23 

137 

40 

6-461  66 

137 

•3« 
'3H 
139 
140 
141 
141 
142 
142 
143 
'43 
'44 
'45 
146 
146 

'47 
148 
148 

'49 
'50 
150 
'5' 
'52 
152 
'53 
153 
'54 
155 
■56 
'57 


4o°oo' 
10 
20 

30 
40 

5" 


41 


42 


43 


44 


45 


10 

2f) 

30 
40 

50 

10 
20 
30 
40 
50 

10 
20 

30 
40 
50 

10 
20 
30 
40 

5<' 

10 
20 
30 


6  461  66 
60  08 

58  50 

■456  9' 

55  32 

53  72 

■452  II 

5"  5f' 

48  88 

■447  25 

45  61 

43  97 

■442  32 

40  66 

3«  99 

■437  32 

35  64 

33  95 

•432  26 

30  56 

28  85 

427  13 
25  4" 
23  67 

■421  93 
20  iS 
18  42 

•416  66 
14  89 
"3  " 

•411  33 

*>9  54 

07  74 

6-405  93 


158 
■58 
'59 
'59 
160 
161 
161 
162 
'63 
164 
164 
■65 
166 
167 
167 
1 6.8 
169 
169 
170 

'7' 
172 

'73 
'73 
'74 
'75 
176 
176 

"77 
178 

1 78 

'79 
180 

181 


Selectioi/  of  stations  for  7oliich   the  results  of  eoiiif>arisoii   of  astrououiie  and  f^eodftic  dalu   uere 

admitted  into  the  equations  of  eondition. 

In  a  preceding  table  there  has  been  exhibitetl  a  comparison  of  the  astronomic  and 
geodetic  latitudes  for  71  stations.  If  all  of  these  were  inclnded  in  the  discnssion.  the 
labor  of  computation  would  be  uiniecessarily  great,  since  practically  the  s;ime  accuracy 
of  the  results  can  be  attained  by  a  judicious  selection  of  a  much  smaller  numlier  of  lati- 
tude stations,  provided  they  are  uniforndy  tlistributed  over  the  whole  region  of  the  arc. 


382  THE    EASTERN    OBLIQUE    ARC. 

The  following  table  contains  these  selected  stations  with  their  geodetic  positions  (to 
the  nearest  half  second),  together  with  the  computed  distances  ^  and  azimuths  a'  to  the 
reference  station  at  Washington,  D.  C.  For  these  stations  the  value,  "S  (A  —  G)  n 
=  +  2"' I,  is  nearlj'  the  same  as  that  previously  derived  from  all  the  stations  after  the 
mean  value  for  each  of  the  6  groups  had  been  introduced  in  place  of  the  separate  values. 


No. 

Name  of  latitude  station. 

Geodetic  lati- 
tude <p'. 

Geodetic  Ion 
gitiide  A'. 

<p'- 

-g, 

A'-; 

9 

0      / 

// 

0 

/      // 

0 

/ 

// 

0     / 

// 

0    / 

// 

0 

/        // 

I 

Calais 

45   II 

04 

67 

16  54 

^6 

15 

49 

- 

9  47 

09 

9  34 

49 

232 

42  56 

2 

Cooper 

44  59 

1 1 

5 

67 

28  03 

+  6 

03 

56-5 

- 

9  36 

00 

9  21 

22 

233 

03   11 

3 

Humpback 

44  51 

49 

68 

06  39 

+  5  56 

34 

- 

8  57 

24 

8  55 

16 

231 

27  55 

4 

Farmingtou 

44  40 

21 

70  09  18  -5 

+  5 

45 

06 

- 

654 

44 '5 

7  42 

59 

224 

19  19 

5 

Mount  Desert 

44  21 

03 

68 

13  39 

f5 

25 

48 

- 

8  50 

24 

■8  32 

35 

233 

42  02 

6 

Mount  Pleasant 

44  01 

35 

70 

49  23 

-f5 

06 

20 

- 

6  14 

40 

6  55 

15 

224 

43  13 

7 

Mount  Independence 

43  45 

32 

70 

19   15 

-1-4 

50 

17 

- 

6  44 

48 

7    GO 

00 

228 

41  55 

8 

Aganienticus 

43   13 

22 

5 

70 

41   34 

+4 

iS 

07 '5 

~- 

6  22 

29 

6  26 

47 

230 

24  31 

9 

Unkonoonuc 

42  5«  58 

71 

35  20 

-h4 

03 

43 

- 

5  2S 

43 

5  47 

45 

227 

27  59 

10 

Thompson 

42  36 

40 

70 

43  50 

+3 

41 

25 

- 

6  20 

13 

6  03 

04 

234 

39  19 

II 

Mount  Tom 

42   14 

28 

72 

38  56 

+3 

19 

13 

- 

4  25 

07 

4  43 

10 

226 

52  28 

12 

Manomet 

41   55 

37 

70 

35  29 

f3 

00 

22 

- 

6  28 

34 

5  46 

18 

240 

51  31 

13 

Sandford 

41   27 

41 

72 

57  00 

+  2 

32 

26 

- 

4  07 

03 

4  02 

33 

232 

31  34 

14 

West  Hills 

40  48 

53 

73 

25  33 

+  r 

53 

38 

"- 

3  38 

30 

3  22 

33 

237 

09  52 

15 

Beacon  Hill 

40  22 

24 

5 

74 

13  42  '5 

+  1 

27 

09 '5 

- 

2  50 

20-5 

2  37 

27 

237 

24  50 

16 

Yard 

39  58 

23 

75 

23  14 

+  1 

03 

08 

- 

I  40  49 

I  40 

14 

231 

36  39 

17 

Principio 

39  35 

34 

5 

76 

00  17 

+0 

40 

19 '5 

- 

I  03 

46 

I  03 

46 

231 

12  50 

18 

Pooles  Island 

39  17 

13 

5 

76 

15  50 

-Ho 

21 

58-5 

- 

0  48 

13 

0  43 

24 

239 

55  48 

19 

Washington  * 

38  55 

15 

77 

04  03 

0  'O 

0  '0 

0 

20 

Cape  Henlopen  L.  H. 

38  46 

40 

75 

05  03-5 

-0 

08 

35 

- 

I  58 

59 '5 

I  33 

04 

275 

53  29 

21 

Clark 

38  18 

39 

78 

00  12 

—0 

36  36 

+ 

0  56 

09 

0  57 

oS 

49 

59  24 

22 

Elliott  Knob 

38  09 

57 

5 

79 

18  52 

--0 

45 

17-5 

+ 

2   14 

49 

I  54 

45 

66 

08  42 

23 

Long  Mountain 

37  17 

25 

5 

79  05  II 

—  r 

37 

49  "5 

-\- 

2  01 

08 

2   16 

35 

43 

45  26 

24 

Moore 

36  23 

51 

5 

80 

17  00 

-2 

31 

23 '5 

-f- 

3    12 

57 

3  35 

02 

44 

24  J5 

25 

Young        ^ 

35  44 

12 

80 

38  52 

^3 

1 1 

03 

j- 

3  34 

49 

4  16 

14 

40 

50  55 

26 

King 

35   12 

09  "5 

81 

18  46 

-3 

43 

05-5 

+ 

4  14 

43 

5  01 

43 

41 

II  54 

27 

Currahee 

34  31 

36 

5 

83 

22  34 

-4 

23 

38-5 

+ 

6  18 

31 

6  41 

44 

47 

16  55 

28 

Sawnee 

34  14 

03 

84 

09  39 

-4 

41 

12 

+ 

7  05 

36 

7  22 

20 

48 

36  15 

29 

Atlanta 

33  44 

56 

84 

23  19  "5 

-5 

10 

19 

i- 

7   19 

16 -5 

7  50 

20 

46 

45  07 

30 

Kahatchee 

33  13 

36 

86 

21  37 

-5 

41 

39 

j- 

9  17 

34 

9  24 

59 

50 

17  08 

31 

Montgomery 

32  22 

37 

86 

18  or 

-6 

32 

38 

-H 

9  13 

58 

9  56 

43 

46  24  3S 

32 

Lower  Peach  Tree 

31  50 

i8 

5 

87 

32  43 

-7 

04 

56-5 

+ 

10  28 

40 

II  04 

59 

47 

31    10 

33 

Coon 

31   14 

48 

88 

05  44 

-7 

40 

27 

+ 

II  01 

41 

II  49  45 

46 

40  41 

34 

Mobile 

30  41 

29 

88 

02  34 

-8 

13 

46 

-f 

10  58 

31 

12  II 

09 

44 

41    4i 

35 

Fort  Morgan 

30  13 

40 

88 

01   24 

-8 

41 

35 

+ 

10  57 

2r 

12  30  30 

43 

II    II 

36 

New  Orleans  (185S) 

29  57 

18 

90  04  25 

-8 

57 

57 

-f- 

13  00 

22 

13  57 

12 

46 

41  IP 

*  United  States  Naval  Obser\'atory,  Georgetown  Heights. 


THK    DKTP:RMINATI()X    ok   THP:    SI'HKROID. 


383 


The  data  for  the  computation  of  tlie  (Hstances  of  the  several  astronomic  lo7i^i- 
tudc  stations  from  the  reference  station  and  of  the  azimuths  of  tlie  latter  from  each  of 
the  stations  are  contained  in  tl»e  following  table: 


No. 

Name  of  loiiKitiuk-  station. 

(U'odftic 

latitude. 

9' 

Oeodotic 

loiiKitude. 

A' 

Ja 

9 

a' 

0      / 

// 

0      / 

f  / 

0 

/ 

// 

0 

r 

// 

0 

/       // 

I 

Calais 

4.S    I' 

04 

67    16 

5) 

9  47 

09 

9  34 

49 

232 

42  5'i 

2 

Bangor 

44  A'^ 

14 

6S  47 

01 

- 

8 

'7 

02 

8 

3" 

58 

229 

i.S  II 

3 

CambridgL' 

42  22 

5' 

■5 

7;   07 

45 

5 

56 

iS 

5 

40 

42 

234 

33  f« 

4 

Caj)e  May 

38  55  46 

■5 

74  55 

48 

2 

08 

'5 

I 

39 

46 

270 

22   17 

5 

r)o\fr 

39  "9 

18 

■5 

75  3' 

24  5 

1 

32 

38  -5 

I 

'3 

'9 

259 

28  40 

6 

Washington  " 

3.S  55 

15 

77  "4 

03 

0 

0 

7 

vStrashiirg 

38  59 

2S 

78  21 

.i9  5 

I 

17 

365 

, 

00 

3^' 

93 

34  20 

8 

Charlotte.svill 

et 

38  01 

56 

78  3> 

2r 

-■ 

I 

27 

18 

I 

26 

40 

51 

42  23 

9 

Statesville 

35  46 

54 

80  53 

40 

+ 

3 

49 

37 

4 

22 

'4 

43 

CJ4  37 

10 

Atlanta 

33  44 

56 

^4  23 

19 '5 

-U 

7 

'9 

16-5 

7 

5' J 

20 

4^^ 

45  03 

II 

Montgomery 

32  22 

37 

86   18 

01 

+ 

9 

'3 

58 

9 

56 

43 

4^ 

24  38 

12 

Lower  Peach 

Tree 

31  50 

18 

5 

87  32 

43 

+  10 

28 

40 

II 

04 

59 

47 

31    10 

13 

Mobile 

3"  41 

29 

88  02 

34 

+ 

10 

5.H 

31 

12 

1 1 

09 

44 

41  45 

14 

New  Orleans 

1H95) 

29  56 

51 

5 

90  04 

12 

+ 

13 

(X> 

09 

13 

57 

22 

46 

39  S"^' 

The  data  for  the  computation  of  the  distances  of  the  several  astnniomic  a:iiiiut/i 
stations  from  the  initial  station  and  of  the  azimuths  of  the  latter  from  the  various  stations 
will    be  found   in  the  following  table,  together  with  the  re.sulting  values  of  H  and  o-'. 

As  was  the  ca.se  with  the  latitudes,  we  have  here  a  .surplus  of  .stations  at  which  astro- 
nomic azimuths  were  mea.sured.  Much  lalxir  ma\-  therefore  be  saved  without  incur- 
ring au}'  sensible  loss  of  accuracy  in  the  results  b\-  the  selection  of  a  more  limited 
number  of  stations  uniformly  distributed,  as  nearh-  as  may  be,  over  the  whole  arc  and 
properly  representing  the  deflection  over  every  part  of  it.  For  these  34  positions  the 
average  value  of  (A-G)  is  i'"9,  the  same  value  found  from  all  the  stations. 


*  United  States  Naval  Observatory.  Georgetown  Heights.  Washington,  D.  C. 
t  McConnick  Observatory. 


384 


THE    EAvSTERN    OBLIQUE    ARC. 


No. 


Name  of  azimuth  station. 


Geodetic  lati- 
tude <p'. 


Geodetic  longi- 
tude A'. 


15 
16 

17 
18 

19 
20 
2! 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 

33 
34 
35 
36 

37 
38 

39 

40 

41 

42 

43 
44 
45 
46 

47 


Cooper 

Humpback 

Mount  Desert 

Mount  Harris 

vSabattus 

-\ganienticus 

Gunstock 

Unkonoonuc 

Blue  Hill 

Mount  Tom 

vSandford 

We.st  Hills 

Mount  Rose 

Yard 

Principio 

Cape  Henlopen  Light-House 

Hill 

Maryland  Heights 

Bull  Run 

Clark 

Long  JMountain 

Elliott  Knob 

Moore 

Young 

King 

Paris 

Currahee 

Atlanta  Middle  Base 

Lavender 

Aurora 

Kahatchee 

Ethridge 

Fort  Morgan 

East  Pascagoula 


44  59  1 1  "5 
44  51  49 
44  21  03 
44  39  53 
44  oS  36 
43  13  22-5 
43  31  02 
42  58  58 
42  12  42 
42  14  29 
41  27  41 
40  48  53 
40  22  01 
39  58  23 
39  35  34 '5 
38  46  40 

38  53  53 

39  20  26 

38  52  51 
38  18  39 

37  17  25-5 

38  09  57 
36  23  5 1  -5 
35  44   12 
35   '  2  25  '5 
34  56  27 
34  31  43 

33  54  19 

34  19  J  7 
34  08  45  '5 
33  13  36 
32  04  44 
30  13  40 
30  20  33  -5 


67  28  03 

68  06  39 

68  13  39 

69  08  56 

70  04  45 

70  4J  34 

71  22  12 
71  35  20 

71  06  53-5 

72  38  56 

72  57  00 

73  25  33 

74  43  26 

75  23  14 

76  00  17 

75  05  03  -5 

76  52  50 

77  43  00 

77  42  13 

78  00  12 

79  05  IT 

79  18  52 

80  17  ai 

80  38  52 

81  iS  46 

82  24  40-5 

83  22  34 

84  I 6  38 

85  17  19 

86  II  01 

86  21  37 

87  "3  29-5 

88  01  24 
88  32  46 


9  21  22 
8  55  16 
8  32  35 
8  13  45 
7  23  II 
6  26  47 
6  16  52 
5  47  45 
5  35  25 
4  43  II 
4  02  33 
3  22  33 
2  18  45 
I  40  14 
I  03  46 

1  33  04 
o  oS  50 
o  39  20 
o  29  48 

0  57  08 

2  16  35 

1  54  45 

3  35  02 

4  16  14 

5  01  31 

5  50  10 

6  41  40 

7  39  52 

8  02  13 

8  44  14 

9  24  59 

10  36  57 
12  30  30 
12  44  17 


233  03  1 1 

231  27  55 
233  42  02 
228  35  51 
227  31  20 

230  24  31 

225  01  01 
227  27  59 

236  01  39 

226  52  19 

232  31  34 

237  09  52 
232  09  32 

231  36  39 
231  12  50 

275  53  29 
278  55  34 
129  20  27 

85  II  54 

49  59  24 

43  45  26 
66  08  42 

44  24  15 

40  50  55 

41  13  54 

45  34  04 
47  17  31 
47  II  II 
52  50  26 
54  21  31 

50  17  08 
47  14  05 

43  1 1  II 

44  43  51 


TIIK   DETERMINATION   OV    Till'.   SPHEROID.  38; 

Coiiitiliiiiuil  01-  ()/>sirT<i/i(iii  I  (/lid/ ions  i/i  ri7'ii/  /nmi  liititiiilf  cinnpariunis. 

/> 

£  ,= -5  "Sr  (-()  •9.S54S  o   i(j6S//  |()i6,si//  •3'7759^' 

c  j=     0-96  +0  ■9X60  ni(i.).S  9 ''Ssos  •  3  "6825 

63=-!  I -83  (  o.  9.S7.S  no97S  9  73.5"  •  3  •6fj.S2 

£4  =  4  I '43  [-0-9927  "■"7.5'^  9-67«)  t-3  M'^^-^ 

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£  c^=     I  -49  -|  o  -9954  -o  -o6cx )  6  -864 1  +  2  -5997 

£.o=-hi-7o  +0-9939  —0-0693  6-1328  +2-4135 

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^12=41-30  +0-9936  —0-0709  49244  20272 

1.3=  1-0 '56  (0-9974  -0-04,51  4 -.1093  •  1  -7109 

?i4=+3'36  -1-0-9980  -0-0399  -3 '2074  •1-3042 

?.5=-3-47  -f  0-9988  -0-0311  -2-4765  10117 

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1,7  =  + 1 -80  +0-9998  o-oii6  —   1-1667  +0-4758 

£,8=  -4 -oo  +0-9999  o  0088  —  0-6352  •0-2619 

£,p=|-I-I5                  ,      +1-0000  n  -OtXTO  0-0000  I      ()-(XXX) 

S2o  =  -|-o-io  +0-9994  0-0217  ;    ()-279o  i)-()978 

?si=— 0-38  (-0-9999  I  0-0103  +     I    0730  0-4466 

S2==+o-43  +0-9992  +0-0246  +   1-35,56  0-5496 

£2,  =  — 3-34  +0-9994  +0-0221  +    28818  — 1  ■;28| 

?24  =  ^3'6i  +0-9984  +0-0353  +4-4X82  1-9447 

£j5=— 9-42  +0-9980  10-0392  -f-  5-6629  -2-5008 

£26=— 3 '84  +0-9973  !  0-0465  (6-6332  2-9595 

£„j=-~i-io  +0-9939  (0-0690  .    7  ■96.54  -3  "5375 

£28  =  —  ! -lo  +0-9923  +0-0776  -r  .S-5469  -3  7925 

£25=— 3-18  +0-9918  -(o-o8oi  J    9-4168  4 -242S 

£^o=— 3-83  +0-9869  +0-1014  -'  10-5494  -4-6986 

£3,  =  —  7  -87  +0  -9870  +0  -  looS  -^12  -024 1  5  -5387 

£3^  =  —  2  -49  +0  -9S33  '  o  ■  1 1 43  t  1 3  - 1 250  6  -0530 

£33  =  +o-65  +0-9816  ;(i-i2ii2  -t-14-2331  —6-6521 

£34  =  — 4-61  +0-9817  101196  :I5-I9i8  —7-2431 

£35= -7 '58  +0-9818  1-0-1194  -15-9952  —77455 

£,,,=  -7-31  +o-9743£  +0-1414?/  .-16-7861/^  — 7-9Si9r' 
4192 — No.  7 — 02 — - — 25 


386  THE    EASTERN    OBLIQUE    ARC. 

Conditional  equations  derived  from  longitude  comparisons. 


77, =+2  78 

+0  -1206? 

+0  -98737 

—  13-3036// 

—  2  -6324- 

?/2=+o-99 

+0-I0I5 

+0  -9899 

—  u  -2689 

—  2  -2298 

V  3  =  +070 

+0  '0697 

+0  -9958 

-  S-0733 

-I  -5975 

'/4=-i  '83 

+0  -0234 

+0  -9998 

—  2  -902 1 

-0  -5743 

'/.-,  =— 470 

+0  '0170 

+0  -9998 

~  2  -0968 

—0-4146 

'/  c=-4  70 

0  "OOOO 

+  I  -OOOO 

0  -OOOO 

o-oooo 

'/7="2-9S 

— 0  "0142 

+0  -9999 

-1-  I  7565 

+0  -3476 

77  ^=-0-83 

-0-OI57 

+0  •999''5 

+  I  -9786 

+0-3915 

V<)=+o7i 

^0  -0390 

+0  -9978 

+  5  '2098 

+  1  -0309 

'7i.,=  ^o-55 

—0  '0708 

+0  -9932 

+  9 '9653 

+  1  -9719 

'Ai  =  — I  '46 

—0  -0859 

+0  -9893 

+  12-5722 

+  2  -4877 

Vi,  =  -2-o6 

-0  -0959 

+0  -9870 

4-14-2656 

+2  -S228 

7i3=+3"04 

— 0  '0972 

+  0-9841 

+ 14  -9586 

H-2  -9599 

7u=~o-62 

-0-1123= 

+0  -9801// 

^17  -7166// 

^3  -S^SS: 

Conditional  equations  derived  from  azimuth  coniparisons. 


7i5=- 

2  -12 

+0  •2359£ 

+0  -8762// 

— 

[3  -0504// 

-2.5823; 

'A6=- 

4 -58 

+0  -2207 

+0  -8797 

- 

12-1795 

—  2  -4100 

717=- 

0  -70 

+0-2198 

+0  -8S80 

- 

r2  -0170 

—2  -3778 

'?i8  =  - 

4-63 

+0-1960 

+0  -8852 

- 

ro-7734 

—  2  -1318 

'7i9=- 

2  -96 

4-0-1747 

+0  -8954 

- 

9  '5081 

-I  -8814 

?720=  + 

0-44 

+0  -1621 

+0-9117 

" 

8  -6702 

—  I  -7156 

7M=- 

6-57 

+0  -1442 

+0  -9079 

- 

7  7540 

-I  -5343 

?^2=  - 

3 '97 

+0-1400 

+0-9173 

- 

7  -4540 

-1-4750 

'7=3  =  - 

o-i8 

+0-1544 

+0  -9300 

- 

8  -0914 

—  I  -6011 

'7=4=- 

7-28 

+0  -1 146 

+0-9318 

— 

6-0119 

-I  -1S96 

7=5=-- 

10  -66 

+0  -1084 

+0  -9464 

- 

5  -5994 

—  I  -1080 

1h6=  — 

5-15 

+0  -0972 

+0  -9593 

- 

4  -9506 

—0  -9796 

'727=+- 

3-14 

+0-0631 

+0  -9692 

- 

3-1873 

—0  '6307 

'7=8=  — 

177 

4-0  -0456 

+0  -9775 

" 

2  -2853 

-0  -4522 

7729=- 

10-78 

+0-0291 

+0  -9856 

- 

I  -4459 

—0  -2861 

'730  =  " 

2-54 

+0  -0552 

+  1  -0025 

- 

2  -6928 

-0-5329 

7731=- 

8-38 

+0  -0052 

+ 1  -0005 

- 

0  -2538 

—0  -0502 

'732=  + 

4-47 

—0-0179 

+0  -9910 

+ 

0  -8830 

+0-1747 

'733  =  + 

3 '04 

— 0  -0177 

+ 1  -0008 

+ 

0  -8638 

+0-1709 

'734  =  + 

1-32 

—0  -0264 

+  1  -0133 

+ 

I  -2729 

+0-2519 

%5=  + 

6  -41 

—0  -0582 

+ 1  '0363 

+ 

2  -7478 

+0  -5437 

»736=~ 

2-66 

—0  -0634 

+  1  -0159 

+ 

3  '0528 

+0  -604 1 

'737=  + 

I  -23 

—0  -0945 

+  1-0571 

+ 

4  -3768 

+0  -8660 

%8=- 

I  -44 

—0-1069 

+  1  -0735 

+ 

4-8751 

+0  -9646 

'739=  + 

3 '40 

—0  -1284 

+ 1  -0S67 

+ 

5  -7809 

+  1-1439 

'740=  + 

1-03 

—0-1626 

+  1  -0922 

+ 

7  -2736 

+  1  -4393 

'741=- 

275 

-0-1939 

+  I-IOI7 

+ 

8  -5856 

-f-i  -6989 

THE    DETERMINATION    OK    THE    SPHEROID.  387 

C  'o)ulUional  cqitalions  derived  from  a-jiinn/h  (oiii/xirisoiis  -ctjiiliiiuefl. 
// 
'742=+5'6i  — o  •2250  ^1-1173  1    9-.Si3()  -1-9417 

743  =  +    2-89  —0-2536  I    I  -1028  .11-1790  •2-2l2(J 

V^i  =  -\'   3 '"7  —0-2823  i  '    lo.S'  -112-3928  4-2-4522 

^5  =  +  4'09  -0-2947  I  1    1315  -112-6422  4-2-5016 

746=+  4 '37  -0-3266  + 1 -1650  H 13  6023  -t- 2 -6916 

'747  =  +  8-72  -0-3775  f-1'2252  4  14  •9407  +2-9564 

'748=+3'3o  —0-3939?  +1-21S7V  ^15-6464^  -f3-096iz' 

/•'oniia/ioii  of  iionnal  equations. 

The  types  of  a  latitude  observation  equation  and  of  a  lonj^itude  and  azimuth  equa- 
tion are: 

i,^=ni-\-ak^br]^cu-\-ev 

then  <f ,  //,  //,  and  t'  are  to  be  determined  so  as  to  make  a  niininnim  tlie  <iuantity 

2(ut  +  a^+bt]+cu+evY+-w2{n-\-a'^-{-b'ti-\-c'u+e'vY 

whence  the  normal  equations: 

o={am)+iv{a'n)  +  [aa']^+{ab']rf+{ac'\ii-i-[ac'\v 
o={bm)  +  za{b'n)  +  \ab-]^+lbb']r)+[bc']u-rlbeyj 
0=  {cm)+w{c'ii)  +  \_ac]q+lbc'\r)^lcc'\u+{ce]v 
0=  {cin)  +  'w(e'H)-\-[ae]^  ^-lbi'\tii-[ce]u^lee'\z' 
where 

[aa']  =  (aa)  A-  ~ai{a'  a' ) 
[ab']={ab)-\-zu(a'b') 

For  equal  weight  to  the  several  equations  ir  becomes  unity,  as  will  be  assumed  in 
the  first  of  our  combinations. 

The  relative  7cei,i;/its  0/  the  observation  equations. 

The  equations  involving  the  comparisons  of  the  latitudes  and  longitudes  may  be 
considered  as  of  fairly  equal  weight,  the  result  of  the  introduction  of  the  telegraphic 
method  for  the  determination  of  differences  of  longitudes;  thus  arcs  of  the  meridian  and 
arcs  of  the  parallel  may  now  be  conil)ined  as  of  equal  importance  as  far  as  the  astronomic 
data  are  concerned. 

It  is  quite  evident,  however,  that  the  azinuithal  equations  are  certainly  of  inferior 
value,  considering  that  they  are  directly  affected  1)\-  the  accunuilation  of  error  in  the 
angular  measures  of  the  triangles  by  means  of  which  the  geodetic  azimuths  are  carried 
forward.  If  unit  weight  is  assigned  to  each  of  the  latitude  and  longituile  equations,  a 
fraction  only  can  be  assigned  for  the  weight  of  an  azinuith  equation.  There  is  no 
principle  by  means  of  which  the  exact  ratio  of  the  weights  could  be  ascertained,  but  the 
comparison  of  the  mean  values  of  the  squares  of  the  <?'s  and  of  the  //'s.  which  shows 
that  the  latter  is  generally  the  larger  of  the  two,  sufficiently  indicates  the  ueed  of  the 
introduction  of  relative  weights.  There  is  no  rea.son  why  the  avera.ge  deflections  in 
the  meridian  and  in  the  prime  vertical  or  in  any  azimuthal  plane  shouKl  be  of  different 
magnitude. 


38S 


THK    EASTKRN    Ol'.LIOUE    ARC. 


The  resultin.iL,^  values  of  the  <?'s  and  //'^,  or  the  remainders,  in  the  equations  for  the 
several  stations  ma}- be  taken  asrepresentinti'  the  actual  hjcal  or  regional  deviations  of  the 
vertical  of  the  geoid  at  these  places  as  compared  with  the  normal  or  geometric  direc- 
tion: in  other  words,  they  exhibit  the  difference  l.)etween  the  disturbed  and  the  regular 
or  undisturbed  direction  of  gravity  within  the  geographic  limits  of  the  investigation. 
As  a  matter  of  course  these  values  are  affected  to  a  relatively  small  extent  by  the 
una\-oidable  errors  of  obser\-atio'.i. 

For  the  case  in  hand,  as  slK)wn  in  the  following  .solution,  we  have  the  mean  value  of 

589-6 


the  .squares  of  the  discrepancies  in  cp  and  A,  ecjual  to 


50 


I  I  '8,  and  the  mean  value  of 


the  .squares  of  the  differences  in  n-,  equal  to 


789-2 
34 


or   about    double    the    former; 


which  indicates  that  the  azimuth  equations  should  not  have  more  than  half  weight. 

This  solution  presents  the  results  for  a  spheroid  representing  the  curvature  of  the 
surface  along  the  arc  without  distinguishing  relatively  between  the  measures  of  lati- 
tudes, longitudes,  and  azimuths. 

Rcsitltiiij^  iiorvial  equations. 
From  the  latitude  observations: 


o=-  74-4532  t  +35-4844=+  0-0953'/+     35-6977" 
0=  —     4  -0791 
t)=— 526  -5026 
0= +253 -3814 

From  the  longitude  observations: 

\  o  •07605—  o"i95o>^ 
+  13-8089 


25  -06432 

+  o  '2032  +  22  -6054  -   9  -7844 

+  2571  -4804  —1 121  -6132 

+  494-2387 


o=-r-  0-4477 
o=-  10-4552 

o=~  49-5751 
o=—  9-8110 

From  the  azimuth  ob.servations: 


10  -2707//- 
40-1059 
414-6253  - 


o=—  17-9120 
o=—  13  -1179 
0= +833 -7203 
0=+  164  -9719 

hence  by  combination: 


I  •1515^-   I  -4576'/-     52  -7266«- 

+  35-1172   +     41  -5066    ^ 

+  2453  -3579  - 


2  -0324?' 

7  -9363 
279-9192 

55  -3890 

10-43312' 
+   8-2132 

+  485  -4576 
+  96  -0600 


1. 


10=-  91  -9175 

Q=  —  27  -6522 
0=^257  -6426 
.0=4-408-5423 

The  solution  gives  — 


-^36 -71 19=-  I -5573'/-     27-2996//-    37-52982' 
+49-1293   +  104-2179  +      6-3651 
+6439-4636  -  356-2364 
+  645-6877 


|=  +  i -895  898      with  residuals  0-0000 
?;  = +0-862  056  0-0000 

«  =  — 0-077  671  6  0-0002 

lz;=— 0-573  878  0-0002 


TIIK    I)KTI-:kMI\.\TI()X    OI'    TIII".    SI'UHkOID. 


3«^9 


whence   we   i^vt    yif  ~2^o' 2   and    tin- eciuatorial    radius  hecomcs  6  ^yJS  2i'/)-4  — 240'3 
6  377  966'2  meters;   we  have  also  i^-7'  (arc  lor/' )  -  — ovxjo  27S  22,  hence  the  new  r - 
o"oo6  768  7  — o'ooo  278  2  — o'oor)  490  5 


(lb  .1 

Let    *  -^  ir   and  or  the  conii)ression         .  then 


:  =fii  ^  Ui^-i  Ui'  ^  <«!■• 


:o'n()3  250  5 


hence    the    compression  — 


the    resuitinti   vahie    of  /'    is  6  377  966'2  —  20  7; 


307 -r/ 

6  357  228'5  meters. 

Snbstitutinji;  tin-  \;dues  lound  for  <?,  //,  n.  and  v  in  tlie  equation^  of  condition  we 
ol)tain  for  each  station  tlie  oulslandinsr  deflections.  Tliese  (luantities  are  also  needed 
for  the  determination  of  the  proliable  errors  of  the  dimensions  of  the  spheroid  just 
obtained  when  these  residuals  are  treated  as  accidental  errors. 


k't'siil/iiii; 

'allies  of  i  and  1/ 

a/  llic  ohscrvhii;  •iUitioiii. 

No 

si; 

lion. 

No 

Sialion 

I 

Calais 

-5  •20 

19 

Washiniilon 

2 

Cooper 

-0  -52 

20 

Cape  Heiilopeii 

3 

Hiunphack 

+  2-32 

21 

Clark 

4 

Fariiiingtoii 

-\-2  '02 

22 

HUiott  Knol) 

5 

Mount  Desert 

-0  77 

23 

LoiiLj  Mountain 

6 

Mount  Pleasant 

—  0  '89 

24 

.Moore 

7 

Mount  Indepen 

lence 

—  2    04 

2,S 

Vounj; 

S 

Ajj;aineuticus 

-  >  '35 

26 

Kiutj 

9 

ITnkoncioiuic 

— 0  61 

27 

Currahee 

in 

Thonipsou 

+  2-63 

2S 

Sawnee 

II 

Mount  Tom 

+  1-27 

29 

.\llama 

12 

Manoniet 

+  2-35 

3" 

Kalialchee 

13 

Sandfonl 

+  1  76 

3' 

Montijoniery 

14 

West  Hills 

+  4  74 

32 

Lower  IV;. ch  Tree 

15 

Beacon  Hill 

- 1   99 

v>3 

Coon 

16 

Yanl 

-5-'2 

34 

Mobile 

17 

Principio 

43-51 

35 

I'orl  Morjjau 

18 

Pooles  Island 

—  2  -21 

36 

New  ()rle:ins 

-t-3  05 
-f2-o6 

-rl  70 

-t-2-55 

-094 

—0-92 
-6-52 
-"  73 

-2-26 
-^2    36 

-fo-47 
-l-ooi 
-3  67 
+  '  93 
+5  '33 
■1-0  '33 
-2-41 
—  2  "07 


390 


THE    EASTERN    OBIJOUE    ARC. 


Resulting  values  of  ^  and  ?/  a  I  the  ohscrviiig  stations — continued, 
station.  ij  No.  Station. 


I* 

Calais 

2 

Bangor 

3 

Cambridge 

4 

Cape  May 

5 

Dover 

6 

Wa.shington 

7 

Stra.sbiirg 

8 

Charlottesville 

9 

Statesville 

lO 

Atlanta 

II 

Montgomery 

12 

Lower  Peach  Tree 

13 

Mobile 

14 

New  Orleans 

i5t 

Cooper 

i6 

Humpback 

I? 

Mount  De.sert 

iS 

Mount  Harris 

19 

Sabattus 

20 

Agamenticus 

21 

Gunstock 

22 

Unkonoonuc 

23 

Blue  Hill 

24 

Mount  Tom 

+6-41 

25 

Sandford 

-8-55 

+4 '19 

26 

West  Hills 

—3-20 

+3  -24 

27 

Mount  Ro.se 

+471 

-0  -38 

28 

Yard 

— 0-46 

-3 '41 

29 

Principio 

—9  '60 

-3  -84 

30 

Cape  Henlopen  Light-House 

—  I  -07 

-2-49 

31 

Hill 

-7-46 

-0  -37 

32 

Maryland  Heights 

+5-13 

-I-0-5I 

33 

Bull  Run 

+  371 

+0  '37 

34 

Clark 

+  1  '90 

-3  "17 

35 

Long  Mountain 

+6-68 

~4-I2 

36 

Elliott  Knob 

—  2-48 

+0  -85 

37 

Moore 

-fl  -12 

-3  '37 

38 

Young 

-1-65 

+  1-58 

39 

King 

+  3-00 

- 1  -07 

40 

Paris 

+0-27 

+  279 

41 

Currahee 

-3-81 

-I  -44 

42 

Atlanta  :Middle  Base 

+4-28 

~o  '04 

43 

Lavender 

+  1  "23 

-^3■2o 

44 

Aurora 

+  I-I2 

-4-04 

45 

Kahatchee 

+  2  -08 

-I  -48 

46 

Ethridge 

+2-15 

+2-46 

47 

Fort  Morgan 

+6 -20 

-5-10 

48 

East  Pascagoula 

+0-6I 

We  have  '^BB  and  .^'/v  before  and  after  chang-e  of  spheroid. 

Old  spheroid.    New  spheroid. 

From  latitude  equations 
From  longitude  equations 
From  azimuth  equations 


506-5 

265  -9 

83-1 

14'  '5 

789  -2 

519-8 

From  all  equations 


I  378-8 


927  -2 


The  precision  of  the  adjusted  or  resulting  value  of  the  length  of  the  equatorial  radius  and  of  the 
compression  as  found  from  the  measure  of  the  arc. 

To  find  tlie  prol^able  errors  of  the  elements  of  the  resulting  spheroid  we  have  to 
determine  the  mean  error  of  a  single  observation  or  that  of  the  unit  of  -weight,  as  well 
as  the  weights  of  the  values  of  ii  and  v  as  obtained  from  the  solution  of  the  normal 
equations,  whence   the   probable  error  of   the  result  for  the  equatorial  radius  a,  and  for 


the  compression 


or  -,  readilv  follows. 


Stibstituting  the  values  of  B,  ?/,  /i- and  :-  resulting  from  the  solution  of  the  normal 
equations  in  the  equations  of  condition,  the  re.siduals  represent  the  respective  deflec- 
tions  at   the   stations.      vSquaring  and  siunming  up  the.se  re.siduals,  we   get  ;«^  =  ii— --• 


*,Values  I  to  14  from  longitude  equations. 


t  Values  15  to  48  from  azinnith  equations. 


THE    DETERMINATION'    OF    THE    Sl'HHkOID. 


39i 


where  ;;/  =  ineaii  error  (jf  the  unit  of  weij^ht,  n  tlie  mniiherof  observations  or  stations,  and 
;/  the  munl)er  of  normal  ecjuationsor  unkncnvns.  Tlie  weiglit  of  any  one  of  the  unknowns 
is  found  in  the  tisual  way  by  means  of  tlie  sohition  of  the  modified  normal  or  weight 
equations;  thus,  for  the  third  unknown  ii  and  for  the  ])recedinj,''  iiyj)othesis  of  equal 
weijj^ht  to  the  ol)ser\'ations  we  have; 

"=  t  3fi  V'ly  '/.       1  'S.Sy.S  '/-•  27  '2996  qn-     }>!  -529^  7i 

0=  49129.^      •       104-2179       r     6-3651 

■  =  16  439  ■46;,6      -356  -2364 

"=  '  64s  -6877 


Here  </„  is  the  reci])rocal  of  the  wei<^lit  of   11  or,  as  usp..dl\'  written.    —       .  and  the  mean 


error  of  u  or  di^^  is  t;iven  1)\-  w,    -  m  y/ h   --  »iy/n  ;   whence  follows  r,  the  probable  error 
of  a,  and  by  the  same  method  that  of  the  compression  is  obtained  from  m  —m^/q  . 

Applying  this  to  the  results  of  h>])othesis  (i  ),  which  assigns  etjual  weight  '  r«'=  i) 

to  the  olxservation  equations,  we  get  ;;/=    /       —  =  ±3"'4o;   the   weight  equations  in 

connection  with  n  and  i<  give: 

and 


(y,=  f  O  -CXX322I3 

173  =  — o  -0003659 
(7„=-l  o  -iXX)i6S2 
(7,  =  +o  -0001092 


q^  =  -*'0  -0018212 
y5=-o -0003946 
^6=4-0  0001092 
^v  =  -^  o  -( « 1 7 1  S,S 


hence  ??i^,=  ±o'044i,  and  the  corresponding  value  ;«,=  i36"4,  and  the  probable  error  of  </ 
or  r^  =  ±92*0  meters.  From  the  second  set  of  weight  equations  we  get ///^  =  rho"  1400  and 
the  corresponding  value  w,  =  ±3'^,  also  the  probable  error  of  r  or  t\=^-±:.2'2.  The  com- 
plete results  by  hypothesis  (  i  )  are  therefore:   Length  of  ecjuatorial  radius.  6  377  966^92 

meters  and  the  compression  ,  , ■ 

'  '•07'6d=2  2 


o'-'/ 


J\csiilli)ii;  splirrohl. 


The  following  is  the  determination  of  a  spheroid  mo.st  nearly  coinciding  with  the 
surface  of  that  part  of  the  United  States  which  is  traversed  by  the  t)bli(iue  arc  from  the 
St.  Croix  River  at  Calais,  Me.,  to  the  delta  of  the  iNIi.ssissippi  River  at  New  Orleans,  La. 

In  consequence  of  the  uncertaint\  respecting  the  proper  weighting  of  the  azinmth 
equations,  four  .sets  of  normal  equations  were  established,  and  the  results  for  equatorial 
radius  and  compression  were  deduced  for  the  several   hypotheses:  ic—  i.   '.■,   '.;,  and  'j. . 

The  normal  e(|ualit)ns  and  results  are  as  slatctl  below: 


o=-   91  -9175 

+3^71194 

I  -5573'/ 

-    27  2996« 

-  37  529^ 

Hypothesis  I 

o=—   27  -6522 

-  49  1293 

^    104-2179 

-      6-3651 

ia=i 

0=4-257  "6426 
0=-!  40S-5423 

-6439  4636 

-356-2364 
-645  6877 

o=—  82  -9615 

+36-13611 

—  0  •8285V 

—      0  -9363// 

-  32  3«32: 

Hypothesis  II 

o  =  -   21  -0932 

-f-31  "5707 

-^     S3  -4646 

-     2  -2585 

za=y2 

«=  — 159  "2176 
0=4-326-0563 

-5212-7846 

-59S  9652 
r597  6577 

39- 


Hypothesis  III 


Hypothesis  IV 


THE    EASTERN    OKLIQUE    ARC 

i-35  '9442= 


o=-  79 '9762 
(1=  iS  -9069 
o=- 29S  -lyog 
0=^-298  -seio 

I  o=-  7«'4''^35 
0=  -  i7-«i3« 
o=-  367  '6476 
o=-r  284-8134 


-  0-5856^ 
r 25  717^ 


+  35  ■S483S     ,'^-  0-4641?/ 
J-22  -7914 


Hypothesis 

Weight  of  azimuth  ecjuations 

Values      from     solution     of 
equations 


Equatorial  radius  in  meters         a 

Probable  error  of  same  r., 

Compression  (rt-6)  /  a  and  prob- 
able error  of  denominator 


+ 1  -89590 
+0  -86206 

-0  -077672 

-o  -573S7S 

6  377  966 

±92 

I 


II 

-f  I  -87994 
+0  -85433 
— o  -038624 
^o  -485852 
6  378  087 
±91 
I 


307 -6^=2 -2  305'5±2-i 


-^  7  ■''^515" 
-^  76  -5468 
+4803-8917 

+  I2-2  454" 
-t"  73  -0880 
-h4599"4452 

HI 

-:-l  -87237 
-^o  -S4018 
—0-015909 
-o  -43476 
6  378  157 
±90 

I 
304-5=bi  -9 


-  30'5744J' 
^     o  -8896 
-679  -8748 
-I-581  -6477 

-  29  -70507- 
-f-     o  -2052 

—720-3296 
-f573  '6427 

+  1-86779 
+  0  -82657 

— o  -0010345 

—  0-401375 

6  378  203 

±90 

I 

303'7± t  -S 


.      .  .  .f  tbi<  table    it  is  evident,  m  the  first  place,  that  xvhatever 

t:/j:^. = - 1;: — :::::r  :::is  *„...  ..l.  ... ... . 

,        .  ,   /      I  ___  V   and,  in  the  secn.l  place,  that  the  cnrvattire  of 

the  Bessehan  spheroid  (^  -^^zr^.-oj' 

angles  thereto;  the  raduts  „  vanes  but  .3,  "^^J^^^^  ^^  '„,i^,^  „„  ^o^ptes- 

rate  7f'=  '/  as  a  limitinj2^  valne.  .    „r„^.prves  a 

r       -if/    /,,//,.c,\-  ///  is  aimarentlv  the  most  acceptable,  as  it  preser\es  a 

I  the  ime  stations  as  in  the  preceding  tabnlaUon  under  Itypoth^tsI^ 


From  comparisons  (jf  <(. 
Hroin  comparisons  of  A'  s 
From  comparisons  of  n'  s 


2h59  2655  266-0  266-0. 

141-5  II 1-6  98-3  ^''-l- 

.Sig-s      ,5(.'if"-3)     !i(.W9)     {(fiifi-S)- 


From  compaiiM)"^  >"  ■'    -  .'-^  -■  -i^v^io 

,  ,■!     1      .,,i,.,,tt  the  weight  J  as  most  smtaDie. 
X„  the  .iscnssion  of  the  or.inance  snrve.  of  ..real  Hrita.n  atul  IrtlanO  Car.e  a.iopts  the  .e  . 


THE   DETERMINATION   OF   THE   SPHEROIU.  393 


I 

-5 '34 

I 

+  5 

•19 

15 

"  39 

2 

-0-65 

2 

^3 

•16 

16 

-219 

3 

-F2-i8 

3 

+  2 

■50 

'7 

+  1  -68 

4 

-M-87 

4 

—  0 

•64 

18 

2-42 

5 

-0-89 

5 

3 

•61 

•9 

0  '91 

6 

—  I  -02 

6 

3 

■85 

20 

2  40 

7 

-2-15 

7 

2 

•31 

21 

4  76 

8 

-1-45 

8 

0 

•21 

22 

-2-lS 

9 

-070 

9 

-f-o 

■96 

23 

•    1  71 

10 

+  2-55 

10 

f-o 

•23 

24 

5  -66 

II 

+  1  -19 

II 

~2 

•07 

25 

911 

12 

4-2-30 

12 

i  2 

•87 

26 

-3  -65 

13 

+  171 

13 

+  2 

•16 

27 

•  4-39 

14 

+  4-68 

14 

—  I 

•81 

28 

-0  63 

15 

-2-03 

29 

-976 

16 

-5 -16 

30 

-'•33 

17 

-r5  '48 

31 

-7  -52 

18 

—2  -24 

32 

-5  19 

19 

+  3  '02 

33 

^3  77 

20 

+1-98 

34 

+  1  -98 

21 

+1  -69 

35 

+6-90 

22 

+  2-53 

36 

-2  24 

23 

—0  -96 

37 

-f  I  "SO 

24 

-0-94 

38 

-I  24 

25 

-6-52 

39 

+  3 '47 

26 

-075 

40 

+090 

27 

+  2-23 

41 

-308 

28 

+  2-34 

42 

4-5   '2 

29 

+  0-44 

43 

+  2  -22 

30 

0-03 

44 

+  2  -21 

31 

-372 

45 

+  3-19 

32 

+  1-87 

46 

+  3-34 

33 

+5  -25 

47 

+  7 '52 

34 

+  0-24 

48 

+  1-99 

35 

~2  -52 

36 

-2-17 

trom 


The  prol^able  error  of  a  sin_e;le  latitude  is  o'674  J  ~ =  ±i""94  as  computed  fi 

^  36  —  4 

the   ^6  latitude  discrepancies  and  tliat  of  a  sin,t;le  latitutle  or  loiiijitude  ob'TA-.''^  "*  "'*  = 

>  5^  —  4 
±i"'90  as  computed  from  the  ^^  latitude  and  the  14  loni^ituile  discrepancies. 

4192 — No.  7 — 02 26 


Comparison  with  Other  Spheroids. 

The  following  table  is  presented  for  convenience  of  reference  or  comparison  of  the 
resnlting  spheroid  with  a  few  other  spheroids  (of  revolution): 

Equatorial  Polar  semi-  ,-„.„„,<.<.e,. 


Spheroid  of —  radius  i;  diameter  b  a  —  h. 

in  meters.  in  meters. 


(a-b)  a. 


Ressel,  1841.      From  10  arcs  of  the  meridian,  total         6  377  397         6  356  079  21  318  1/29915 

amplitude  50°  34'.  ~-^     "' 

Clarke,  1858.*  Special  spheroid  for  surface  of  Great         6  37S  494         6  355  746  22  74S  1/280-4 

-f-QO  ~^~S  '\ 

Britain  and  Ireland.     Range  in  latitude  12°,  the  ^  ^ 

same  in  longitude;  75  astronomic  stations. 
Clarke,    1S66.      I'rom    five   meridional    arcs,   total  6  37S  206         6  356  5S4  21   622  1/295 'o 

amplitude  76°  35'. 
Clarke,  1S80.*    From  five  meridional  arcs  and  Ion-         6  37S   249         6  356  515  2\   734  1/293-5 

gitudinal  measures,   total    amplitude  88°   59' -8 

equatorial  degrees. 
U.  vS.  Coast  and  Geodetic  vSurve}-,  1900.     Eastern         6  37S  157         6  357  210  20  947  1/304  "5 

Oblique  Arc  of  the  United  vStates.     Total  ampli-  — ^^  ~'^ 

tude  23°  31';  84  astronomic  stations. 
Harkness,  1891.     From  "The  Solar  Parallax  and         6  377  972         6  356  727  2!   245  1/300-2 

Related  Constants,"  Washington,  1891,  p.  138.  ~     ^  " 


*  For  conversion  of  English  feet  into  meters  Clarke's  determination  of  1S66  wa.s  used,  viz:  r  ft.  =0-30479727  m, 

I  m.  =3-28086933  ft. 

394 
0 


1 


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